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Jing Mao

Publications and source records attributed to Jing Mao.

At least 37 records · Page 2Linked to original sources
arXiv2021

Isoperimetric Bounds for Eigenvalues of the Wentzell-Laplace, the Laplacian and a biharmonic Steklov Problem

In this paper, we prove some isoperimetric bounds for lower order eigenvalues of the Wentzell-Laplace operator on bounded domains of a Euclidean space or a Hadamard manifold, of the Laplacian on closed hypersurfaces of a Euclidean space or a Hadamard manifold, and of a biharmonic Steklov problem on bounded domains of a Euclidean space. Especially, interesting rigidity results can be obtained if sharp bounds were achieved.

math.DG↗
arXiv2021

Estimates for eigenvalues of the Neumann and Steklov problems

We prove Li-Yau-Kröger type bounds for Neumann-type eigenvalues of the poly-harmonic operator and of the biharmonic operator on bounded domains in a Euclidean space. We also prove sharp estimates for lower order eigenvalues of a biharmonic Steklov problem and of the Laplacian, which directly implies two sharp Reilly-type inequalities for the corresponding first nonzero eigenvalue.

math.DG↗
arXiv2021

An anisotropic inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$

In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $\mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space $\mathbb{R}^{n+1}_{1}$ along an anisotropic inverse mean curvature flow with the vanishing Neumann boundary condition, and prove that this flow exists for all the time. Moreover, we can show that, after suitable rescaling, the evolving spacelike graphic hypersurfaces converge smoothly to a piece of hyperbolic plane of center at origin and prescribed radius, which actually corresponds to a constant function defined over the piece of $\mathscr{H}^{n} (1)$, as time tends to infinity. Clearly, this conclusion is an extension of our previous work [2].

math.DG↗
arXiv2021

Translating solutions for a class of quasilinear parabolic initial boundary value problems in Lorentz-Minkowski plane $\mathbb{R}^{2}_{1}$

In this paper, we investigate the evolution of spacelike curves in Lorentz-Minkowski plane $\mathbb{R}^{2}_{1}$ along prescribed geometric flows (including the classical curve shortening flow or mean curvature flow as a special case), which correspond to a class of quasilinear parabolic initial boundary value problems, and can prove that this flow exists for all time. Moreover, we can also show that the evolving spacelike curves converge to a spacelike straight line or a spacelike Grim Reaper curve as time tends to infinity.

math.DG↗
arXiv2021

A class of inverse curvature flows for star-shaped hypersurfaces evolving in a cone

Given a smooth convex cone in the Euclidean $(n+1)$-space ($n\geq2$), we consider strictly mean convex hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If those hypersurfaces inside the cone evolve by a class of inverse curvature flows, then, by using the convexity of the cone in the derivation of the gradient and Hölder estimates, we can prove that this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a piece of a round sphere as time tends to infinity.

math.DG↗
arXiv2021

A stability result for translating space-like graphs in Lorentz manifolds

In this paper, we investigate space-like graphs defined over a domain $Ω\subset M^{n}$ in the Lorentz manifold $M^{n}\times\mathbb{R}$ with the metric $-ds^{2}+σ$, where $M^{n}$ is a complete Riemannian $n$-manifold with the metric $σ$, $Ω$ has piecewise smooth boundary, and $\mathbb{R}$ denotes the Euclidean $1$-space. We can prove an interesting stability result for translating space-like graphs in $M^{n}\times\mathbb{R}$ under a conformal transformation.

math.DG↗
arXiv2020

Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order

In this paper, we investigate the buckling problem of the drifting Laplacian of arbitrary order on a bounded connected domain in complete smooth metric measure spaces (SMMSs) supporting a special function, and successfully get a general inequality for its eigenvalues. By applying this general inequality, if the complete SMMSs considered satisfy some curvature constraints, we can obtain a universal inequalities for eigenvalues of this buckling problem.

math.DG↗
arXiv2020

Existence and uniqueness of solutions to the constant mean curvature equation with nonzero Neumann boundary data in product manifold $M^{n}\times\mathbb{R}$

In this paper, we can prove the existence and uniqueness of solutions to the constant mean curvature (CMC for short) equation with nonzero Neumann boundary data in product manifold $M^{n}\times\mathbb{R}$, where $M^{n}$ is an $n$-dimensional ($n\geq2$) complete Riemannian manifold with nonnegative Ricci curvature, and $\mathbb{R}$ is the Euclidean $1$-space. Equivalently, this conclusion gives the existence of CMC graphic hypersurfaces defined over a compact strictly convex domain $Ω\subset M^{n}$ and having arbitrary contact angle.

math.DG↗
arXiv2020

Translating solutions of the nonparametric mean curvature flow with nonzero Neumann boundary data in product manifold $M^{n}\times\mathbb{R}$

In this paper, we can prove the existence of translating solutions to the nonparametric mean curvature flow with nonzero Neumann boundary data in a prescribed product manifold $M^{n}\times\mathbb{R}$, where $M^{n}$ is an $n$-dimensional ($n\geq2$) complete Riemannian manifold with nonnegative Ricci curvature, and $\mathbb{R}$ is the Euclidean $1$-space.

math.DG↗
arXiv2019

Eigenvalue comparisons in Steklov eigenvalue problem and some other eigenvalue estimates

In this paper, two interesting eigenvalue comparison theorems for the first non-zero Steklov eigenvalue of the Laplacian have been established for manifolds with radial sectional curvature bounded from above. Besides, sharper bounds for the first non-zero eigenvalue of the Wentzell eigenvalue problem of the weighted Laplacian, which can be seen as a natural generalization of the classical Steklov eigenvalue problem, have been obtained.

math.DG↗
arXiv2018

High Reversibility of Lattice Oxygen Redox in Na-ion and Li-ion Batteries Quantified by Direct Bulk Probes of both Anionic and Cationic Redox Reactions

The reversibility and cyclability of anionic redox in battery electrodes hold the key to its practical employments. Here, through mapping of resonant inelastic X-ray scattering (mRIXS), we have independently quantified the evolving redox states of both cations and anions in Na2/3Mg1/3Mn2/3O2. The bulk-Mn redox emerges from initial discharge and is quantified by inverse-partial fluorescence yield (iPFY) from Mn-L mRIXS. Bulk and surface Mn activities likely lead to the voltage fade. O-K super-partial fluorescence yield (sPFY) analysis of mRIXS shows 79% lattice oxygen-redox reversibility during initial cycle, with 87% capacity sustained after 100 cycles. In Li1.17Ni0.21Co0.08Mn0.54O2, lattice-oxygen redox is 76% initial-cycle reversible but with only 44% capacity retention after 500 cycles. These results unambiguously show the high reversibility of lattice-oxygen redox in both Li-ion and Na-ion systems. The contrast between Na2/3Mg1/3Mn2/3O2 and Li1.17Ni0.21Co0.08Mn0.54O2 systems suggests the importance of distinguishing lattice-oxygen redox from other oxygen activities for clarifying its intrinsic properties.

physics.chem-ph↗
arXiv2018

Translating surfaces of the non-parametric mean curvature flow in Lorentz manifold $M^{2}\times\mathbb{R}$

In this paper, for the Lorentz manifold $M^{2}\times\mathbb{R}$, with $M^{2}$ a $2$-dimensional complete surface with nonnegative Gaussian curvature, we investigate its space-like graphs over compact strictly convex domains in $M^{2}$, which are evolving by the non-parametric mean curvature flow with prescribed contact angle boundary condition, and show that solutions converge to ones moving only by translation.

math.DG↗
arXiv2017

Hyperbolic inverse mean curvature flow

In this paper, we prove the short-time existence of hyperbolic inverse (mean) curvature flow (with or without the specified forcing term) under the assumption that the initial compact smooth hypersurface of $\mathbb{R}^{n+1}$ ($n\geqslant2$) is mean convex and star-shaped. Several interesting examples and some hyperbolic evolution equations for geometric quantities of the evolving hypersurfaces have been shown. Besides, under different assumptions for the initial velocity, we can get the expansion and the convergence results of a hyperbolic inverse mean curvature flow in the plane $\mathbb{R}^2$, whose evolving curves move normally.

math.DG↗
arXiv2017

Inverse mean curvature flow inside a cone in warped products

Given a convex cone in the \emph{prescribed} warped product, we consider hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If those hypersurfaces inside the cone evolve along the inverse mean curvature flow, then, by using the convexity of the cone, we can prove that this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a piece of round sphere as time tends to infinity.

math.DG↗