arXiv subjects

Yong Wei

Publications and source records attributed to Yong Wei.

At least 37 records · Page 2Linked to original sources

arXiv2023

A complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space

In this paper, we study the locally constrained inverse curvature flow for hypersurfaces in the half-space with $θ$-capillary boundary, which was recently introduced by Wang-Weng-Xia. Assume that the initial hypersurface is strictly convex with the contact angle $θ\in (0,π/2]$. We prove that the solution of the flow remains to be strictly convex for $t>0$, exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in the half-space with the contact angle $θ\in(0,π/2]$. Along the proof, we develop a new tensor maximum principle for parabolic equations on compact manifold with proper Neumann boundary condition.

math.DG↗

arXiv2023

Detection of magnetospheric ion drift patterns at Mars

Mars lacks a global magnetic field, and instead possesses small-scale crustal magnetic fields, making its magnetic environment fundamentally different from intrinsic magnetospheres like those of Earth or Saturn. Here we report the discovery of magnetospheric ion drift patterns, typical of intrinsic magnetospheres, at Mars usingmeasurements fromMarsAtmosphere and Volatile EvolutioNmission. Specifically, we observewedge-like dispersion structures of hydrogen ions exhibiting butterfly-shaped distributions within the Martian crustal fields, a feature previously observed only in planetary-scale intrinsic magnetospheres. These dispersed structures are the results of driftmotions that fundamentally resemble those observed in intrinsic magnetospheres. Our findings indicate that the Martian magnetosphere embodies an intermediate case where both the unmagnetized and magnetized ion behaviors could be observed because of the wide range of strengths and spatial scales of the crustal magnetic fields around Mars.

astro-ph.EP↗

arXiv2023

Chemical Environment Adaptive Learning for Optical Band Gap Prediction of Doped Graphitic Carbon Nitride Nanosheets

This study presents a novel Machine Learning Algorithm, named Chemical Environment Graph Neural Network (ChemGNN), designed to accelerate materials property prediction and advance new materials discovery. Graphitic carbon nitride (g-C3N4) and its doped variants have gained significant interest for their potential as optical materials. Accurate prediction of their band gaps is crucial for practical applications, however, traditional quantum simulation methods are computationally expensive and challenging to explore the vast space of possible doped molecular structures. The proposed ChemGNN leverages the learning ability of current graph neural networks (GNNs) to satisfactorily capture the characteristics of atoms' local chemical environment underlying complex molecular structures. Our benchmark results demonstrate more than 100% improvement in band gap prediction accuracy over existing GNNs on g-C3N4. Furthermore, the general ChemGNN model can precisely foresee band gaps of various doped g-C3N4 structures, making it a valuable tool for performing high-throughput prediction in materials design and development.

physics.chem-ph↗

arXiv2023

A Heintze-Karcher type inequality in hyperbolic space

In this paper, we prove a new Heintze-Karcher type inequality for shifted mean convex hypersurfaces in hyperbolic space. As applications, we prove an Alexandrov type theorem for closed embedded hypersurfaces with constant shifted $k$th mean curvature in hyperbolic space. Furthermore, a uniqueness result for $h$-convex hypersurfaces satisfying certain curvature equations is obtained.

math.DG↗

arXiv2023

Volume preserving Gauss curvature flow of convex hypersurfaces in the hyperbolic space

We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1} (n\geq 2)$ with the speed given by arbitrary positive power $α$ of the Gauss curvature. We prove that if the initial hypersurface is convex, then the smooth solution of the flow remains convex and exists for all positive time $t\in [0,\infty)$. Moreover, we apply a result of Kohlmann which characterises the geodesic ball using the hyperbolic curvature measures and an argument of Alexandrov reflection to prove that the flow converges to a geodesic sphere exponentially in the smooth topology. This can be viewed as the first result for non-local type volume preserving curvature flows for hypersurfaces in the hyperbolic space with only convexity required on the initial data.

math.DG↗

arXiv2023

Geometric inequalities involving three quantities in warped product manifolds

In this paper, we establish two families of sharp geometric inequalities for closed hypersurfaces in space forms or other warped product manifolds. Both families of inequalities compare three distinct geometric quantities. The first family concerns the $k$-th boundary momentum, area, and weighted volume, and has applications to Weinstock-type inequalities for Steklov or Wentzell eigenvalues on star-shaped mean convex domains. This generalizes the main results of [12]. The second family involves a weighted $k$-th mean curvature integral and two distinct quermassintegrals and extends the authors' recent work [33] with G. Wheeler and V.-M. Wheeler.

math.DG↗

arXiv2023

Shifted inverse curvature flows in hyperbolic space

We introduce the shifted inverse curvature flow in hyperbolic space. This is a family of hypersurfaces in hyperbolic space expanding by $F^{-p}$ with positive power $p$ for a smooth, symmetric, strictly increasing and $1$-homogeneous curvature function $f$ of the shifted principal curvatures with some concavity properties. We study the maximal existence and asymptotical behavior of the flow for horo-convex hypersurfaces. In particular, for $0<p\leq 1$ we show that the limiting shape of the solution is always round as the maximal existence time is approached. This is in contrast to the asymptotical behavior of the (non-shifted) inverse curvature flow, as Hung and Wang [18] constructed a counterexample to show that the limiting shape of inverse curvature flow in hyperbolic space is not necessarily round.

math.DG↗

arXiv2022

On the mean curvature type flow for convex capillary hypersurfaces in the ball

In this paper, we study the mean curvature type flow for hypersurfaces in the unit Euclidean ball with capillary boundary, which was introduced by Wang-Xia and Wang-Weng. We show that if the initial hypersurface is strictly convex, then the solution of this flow is strictly convex for $t>0$, exists for all positive time and converges smoothly to a spherical cap. As an application, we prove a family of new Alexandrov-Fenchel inequalities for convex hypersurfaces in the unit Euclidean ball with capillary boundary.

math.DG↗

arXiv2021

Review of Mercury's Dynamic Magnetosphere: Post-MESSENGER Era and Comparative Magnetospheres

This review summarizes the research of Mercury's magnetosphere in the Post-MESSENGER era and compares its dynamics to those in other planetary magnetospheres, especially to those in Earth's magnetosphere. This review starts by introducing the planet Mercury, including its interplanetary environment, magnetosphere, exosphere, and conducting core. The frequent and intense magnetic reconnection on the dayside magnetopause, which is represented by the flux transfer event "shower", is reviewed on how they depend on magnetosheath plasma beta and magnetic shear angle across the magnetopause, following by how they contribute to the flux circulation and magnetosphere-surface-exosphere coupling. In the next, the progress of Mercury's magnetosphere under extreme solar events, including the core induction and the reconnection erosion on the dayside magnetosphere, the responses of the nightside magnetosphere, are reviewed. Then, the dawn-dusk properties of the plasma sheet, including the features of the ions, the structure of the current sheet, and the dynamics of magnetic reconnection, are summarized. The last topic reviews the particle energization in Mercury's magnetosphere, which includes the energization of the Kelvin-Helmholtz waves on the magnetopause boundaries, reconnection-generated magnetic structures, and the cross-tail electric field. In each chapter, the last section discusses the open questions related with each topic, which can be considered by the simulations and the future spacecraft mission. We close by summarizing the future BepiColombo opportunities, which is a joint mission between ESA and JAXA, and is en route to Mercury.

physics.space-ph↗

arXiv2021

Anisotropic curvature measures and volume preserving flows

In the first part of this paper, we develop the theory of anisotropic curvature measures for convex bodies in the Euclidean space. It is proved that any convex body whose boundary anisotropic curvature measure equals a linear combination of other lower order anisotropic curvature measures with nonnegative coefficients is a scaled Wulff shape. This generalizes the classical results by Schneider [Comment. Math. Helv. \textbf{54} (1979), 42--60] and by Kohlmann [Arch. Math. (Basel) \textbf{70} (1998), 250--256] to the anisotropic setting. The main ingredients in the proof are the generalized anisotropic Minkowski formulas and an inequality of Heintze--Karcher type for convex bodies. In the second part, we consider the volume preserving flow of smooth closed convex hypersurfaces in the Euclidean space with speed given by a positive power $α$ of the $k$th anisotropic mean curvature plus a global term chosen to preserve the enclosed volume of the evolving hypersurfaces. We prove that if the initial hypersurface is strictly convex, then the solution of the flow exists for all time and converges to the Wulff shape in the Hausdorff sense. The characterization theorem for Wulff shapes via the anisotropic curvature measures will be used crucially in the proof of the convergence result. Moreover, in the cases $k=1$, $n$ or $α\geq k$, we can further improve the Hausdorff convergence to the smooth and exponential convergence.

math.DG↗

arXiv2021

A fully nonlinear locally constrained anisotropic curvature flow

Given a smooth positive function $F\in C^{\infty}(\mathbb{S}^n)$ such that the square of its positive $1$-homogeneous extension on $\mathbb{R}^{n+1}\setminus \{0\}$ is uniformly convex, the Wulff shape $W_F$ is a smooth uniformly convex body in the Euclidean space $\mathbb{R}^{n+1}$ with $F$ being the support function of the boundary $\partial W_F$. In this paper, we introduce the fully nonlinear locally constrained anisotropic curvature flow \begin{equation*} \frac{\partial }{\partial t}X=(1-E_k^{1/k}σ_F)ν_F,\quad k=2,\cdots,n \end{equation*} in the Euclidean space, where $E_k$ denotes the normalized $k$th anisotropic mean curvature with respect to the Wulff shape $W_F$, $σ_F$ the anisotropic support function and $ν_F$ the outward anisotropic unit normal of the evolving hypersurface. We show that starting from a smooth, closed and strictly convex hypersurface in $\mathbb{R}^{n+1}$ ($n\geq 2$), the smooth solution of the flow exists for all positive time and converges smoothly and exponentially to a scaled Wulff shape. A nice feature of this flow is that it improves a certain isoperimetric ratio. Therefore by the smooth convergence of the above flow, we provide a new proof of a class of the Alexandrov--Fenchel inequalities for anisotropic mixed volumes of smooth convex domains in the Euclidean space.

math.DG↗

arXiv2021

On an inverse curvature flow in two-dimensional space forms

We study the evolution of compact convex curves in two-dimensional space forms. The normal speed is given by the difference of the weighted inverse curvature with the support function, and in the case where the ambient space is the Euclidean plane, is equivalent to the standard inverse curvature flow. We prove that solutions exist for all time and converge exponentially fast in the smooth topology to a standard round geodesic circle. This has a number of consequences: first, to prove the isoperimetricinequality; second, to establish a range of weighted geometric inequalities; and third, to give a counterexample to the $n=2$ case of a conjecture of Girão-Pinheiro.

math.DG↗

arXiv2020

Locally constrained curvature flows and geometric inequalities in hyperbolic space

In this paper, we first study the locally constrained curvature flow of hypersurfaces in hyperbolic space, which was introduced by Brendle, Guan and Li [7]. This flow preserves the $m$th quermassintegral and decreases $(m+1)$th quermassintegral, so the convergence of the flow yields sharp Alexandrov-Fenchel type inequalities in hyperbolic space. Some special cases have been studied in [7]. In the first part of this paper, we show that h-convexity of the hypersurface is preserved along the flow and then the smooth convergence of the flow for h-convex hypersurfaces follows. We then apply this result to establish some new sharp geometric inequalities comparing the integral of $k$th Gauss-Bonnet curvature of a smooth h-convex hypersurface to its $m$th quermassintegral (for $0\leq m\leq 2k+1\leq n$), and comparing the weighted integral of $k$th mean curvature to its $m$th quermassintegral (for $0\leq m\leq k\leq n$). In particular, we give an affirmative answer to a conjecture proposed by Ge, Wang and Wu in 2015. In the second part of this paper, we introduce a new locally constrained curvature flow using the shifted principal curvatures. This is natural in the context of h-convexity. We prove the smooth convergence to a geodesic sphere of the flow for h-convex hypersurfaces, and provide a new proof of the geometric inequalities proved by Andrews, Chen and the third author of this paper in 2018. We also prove a family of new sharp inequalities involving the weighted integral of $k$th shifted mean curvature for h-convex hypersurfaces, which as application implies a higher order analogue of Brendle, Hung and Wang's [8] inequality.

math.DG↗

arXiv2020

Contraction of surfaces in hyperbolic space and in sphere

In this paper, we consider the contracting curvature flow of smooth closed surfaces in $3$-dimensional hyperbolic space and in $3$-dimensional sphere. In the hyperbolic case, we show that if the initial surface $M_0$ has positive scalar curvature, then along the flow by a positive power $α$ of the mean curvature $H$, the evolving surface $M_t$ has positive scalar curvature for $t>0$. By assuming $α\in [1,4]$, we can further prove that $M_t$ contracts a point in finite time and become spherical as the final time is approached. We also show the same conclusion for the flows by powers of scalar curvature and by powers of Gauss curvature provided that the power $α\in [1/2,1]$. In the sphere case, we show that the flow by a positive power $α$ of mean curvature contracts strictly convex surface in $\mathbb{S}^3$ to a round point in finite time if $α\in [1,5]$. The same conclusion also holds for the flow by powers of Gauss curvature provided that the power $α\in [1/2,1]$.

math.DG↗

arXiv2018

Surfaces expanding by non-concave curvature functions

In this paper, we first investigate the flow of convex surfaces in the space form $\mathbb{R}^3(κ)~(κ=0,1,-1)$ expanding by $F^{-α}$, where $F$ is a smooth, symmetric, increasing and homogeneous of degree one function of the principal curvatures of the surfaces and the power $α\in(0,1]$ for $κ=0,-1$ and $α=1$ for $κ=1$. By deriving that the pinching ratio of the flow surface $M_t$ is no greater than that of the initial surface $M_0$, we prove the long time existence and the convergence of the flow. No concavity assumption of $F$ is required. We also show that for the flow in $\mathbb{H}^3$ with $α\in (0,1)$, the limit shape may not be necessarily round after rescaling.

math.DG↗

arXiv2018

Volume preserving flow and Alexandrov-Fenchel type inequalities in hyperbolic space

In this paper, we study flows of hypersurfaces in hyperbolic space, and apply them to prove geometric inequalities. In the first part of the paper, we consider volume preserving flows by a family of curvature functions including positive powers of $k$-th mean curvatures with $k=1,\cdots,n$, and positive powers of $p$-th power sums $S_p$ with $p>0$. We prove that if the initial hypersurface $M_0$ is smooth and closed and has positive sectional curvatures, then the solution $M_t$ of the flow has positive sectional curvature for any time $t>0$, exists for all time and converges to a geodesic sphere exponentially in the smooth topology. The convergence result can be used to show that certain Alexandrov-Fenchel quermassintegral inequalities, known previously for horospherically convex hypersurfaces, also hold under the weaker condition of positive sectional curvature. In the second part of this paper, we study curvature flows for strictly horospherically convex hypersurfaces in hyperbolic space with speed given by a smooth, symmetric, increasing and homogeneous degree one function $f$ of the shifted principal curvatures $λ_i=κ_i-1$, plus a global term chosen to impose a constraint on the quermassintegrals of the enclosed domain, where $f$ is assumed to satisfy a certain condition on the second derivatives. We prove that if the initial hypersurface is smooth, closed and strictly horospherically convex, then the solution of the flow exists for all time and converges to a geodesic sphere exponentially in the smooth topology. As applications of the convergence result, we prove a new rigidity theorem on smooth closed Weingarten hypersurfaces in hyperbolic space, and a new class of Alexandrov-Fenchel type inequalities for smooth horospherically convex hypersurfaces in hyperbolic space.

math.DG↗

arXiv2018

Quermassintegral preserving curvature flow in Hyperbolic space

We consider the quermassintegral preserving flow of closed \emph{h-convex} hypersurfaces in hyperbolic space with the speed given by any positive power of a smooth symmetric, strictly increasing, and homogeneous of degree one function $f$ of the principal curvatures which is inverse concave and has dual $f_*$ approaching zero on the boundary of the positive cone. We prove that if the initial hypersurface is \emph{h-convex}, then the solution of the flow becomes strictly \emph{h-convex} for $t>0$, the flow exists for all time and converges to a geodesic sphere exponentially in the smooth topology.

math.DG↗

arXiv2018

New pinching estimates for Inverse curvature flows in space forms

We prove new pinching estimate for the inverse curvature flow of strictly convex hypersurfaces in the space form $N$ of constant sectional curvature $K_N$ with speed given by $F^{-α}$, where $α\in (0,1]$ for $K_N=0,-1$ and $α=1$ for $K_N=1$, $F$ is a smooth, symmetric homogeneous of degree one function which is inverse concave and has dual $F_*$ approaching zero on the boundary of the positive cone $Γ_+$. We show that the ratio of the largest principal curvature to the smallest principal curvature of the flow hypersurface is controlled by its initial value. This can be used to prove the smooth convergence of the flow.

math.DG↗