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Xiaojuan Chen

Publications and source records attributed to Xiaojuan Chen.

14 recordsLinked to original sources
arXiv2026

$L_p$ Brunn-Minkowski inequality for weighted dual quermassintegrals

We investigate the $L_p$ Brunn-Minkowski inequality for dual quermassintegrals in weighted measure spaces, which is a special class of rotationally invariant measures proposed by Cordero-Erausquin and Rotem [Ann. Probab., {\bf 51} (2023)]. Specifically, the weighted dual quermassintegral is defined by integrating the radial density $|x|^{q-n}ϕ(|x|)$ for $q\in(0,n]$, where $ϕ$ is a positive radially non-increasing weight, it recovers the classical dual quermassintegral when $ϕ\equiv1$. For $p\geq1$, we prove the $L_p$ Brunn-Minkowski inequality with concavity exponent $p/q$ under the condition that $t\mapsto\logϕ(e^t)$ is concave, which is exactly the natural convexity condition from Cordero-Erausquin and Rotem's paper in general, improving the exponent $1/n$ when $p=1$. For $p\in(0,1)$, we obtain the result with exponent $p/q$ under more strictly weight assumptions, together with explicit lower bounds for the admissible range of $p$.

math.MG↗
arXiv2026

$L_p$ Minkowski problem and Brunn-Minkowski inequality for dual quermassintegrals

This paper studies the core problems in the $L_p$ dual Brunn-Minkowski theory, encompassing the $L_p$ Minkowski problem and $L_p$ Brunn-Minkowski inequality for dual quermassintegrals. For the case $0<p<q\leq n$, we establish $C^0$ estimates for the $L_p$ dual Minkowski problem without symmetric assumptions, thereby resolving a related problem proposed by Böröczky-Chen-Liu-Saroglou in the smooth sense. We further prove the uniqueness of smooth solutions under appropriate conditions, provided the density function is sufficiently close to a constant in the Hölder norm. Finally, exploiting the fact that the uniqueness of the Minkowski type problem is equivalent to the validity of the Brunn-Minkowski inequality in a certain sense, we study the $L_p$ Brunn-Minkowski inequality for dual quermassintegrals for origin-symmetric convex bodies with $p<q$.

math.AP↗
arXiv2026

CrownGen: Patient-customized Crown Generation via Point Diffusion Model

Digital crown design remains a labor-intensive bottleneck in restorative dentistry. We present CrownGen, a generative framework that automates patient-customized crown design using a denoising diffusion model on a novel tooth-level point cloud representation. The system employs two core components: a boundary prediction module to establish spatial priors and a diffusion-based generative module to synthesize high-fidelity morphology for multiple teeth in a single inference pass. We validated CrownGen through a quantitative benchmark on 496 external scans and a clinical study of 26 restoration cases. Results demonstrate that CrownGen surpasses state-of-the-art models in geometric fidelity and significantly reduces active design time. Clinical assessments by trained dentists confirmed that CrownGen-assisted crowns are statistically non-inferior in quality to those produced by expert technicians using manual workflows. By automating complex prosthetic modeling, CrownGen offers a scalable solution to lower costs, shorten turnaround times, and enhance patient access to high-quality dental care.

cs.CV↗
arXiv2025

Second order estimates for $χ$-semi convex solutions of Hessian equations on Hermitian manifolds

In this paper, we establish the modified concavity inequality for complex Hessian equations under the semi-convexity assumption inspired by Lu \cite{Lu23} and Zhang \cite{Z24} for real case. Then second order estimates for admissible solutions of complex Hessian equations on compact Hermitian manifolds with both sides of equations depending on gradient terms are obtained by taking advantage of the crucial inequality.

math.AP↗
arXiv2025

The $L_p$-dual Christoffel-Minkowski problem for the case $p\geq q$

In this paper, we consider a class of Hessian equations associated to the $L_p$-dual Christoffel-Minkowski problem for the case $p\geq q$. By combining the tools of constant rank theorem, the a priori estimates and the continuity method, we obtain the existence and uniqueness for strictly spherical convex solutions to the $L_p$-dual Christoffel-Minkowski problem.

math.AP↗
arXiv2024

$k$-convex hypersurfaces with prescribed Weingarten curvature in warped product manifolds

In this paper, we consider Weingarten curvature equations for $k$-convex hypersurfaces with $n<2k$ in a warped product manifold $\overline{M}=I\times_λM$. Based on the conjecture proposed by Ren-Wang in \cite{Ren2}, which is valid for $k\geq n-2$, we derive curvature estimates for equation $σ_k(κ)= ψ(V, ν(V))$ through a straightforward proof. Furthermore, we also obtain an existence result for the star-shaped compact hypersurface $Σ$ satisfying the above equation by the degree theory under some sufficient conditions.

math.AP↗
arXiv2024

Dirichlet problem for degenerate Hessian quotient type curvature equations

In the paper, we prove the existence and uniqueness results of the $C^{1,1}$ regular graphic hypersurface for Dirichlet problem of a class of degenerate Hessian quotient type curvature equations under the condition $ψ^{\frac{1}{k-l}}\in C^{1,1}(\overlineΩ\times\mathbb{R}\times\mathbb{S}^n)$. Specially, we also consider the second order derivative estimates for the corresponding degenerate Hessian type curvature equations under the optimal condition $ψ^{\frac{1}{k-1}}\in C^{1,1}(\overlineΩ\times\mathbb{R}\times\mathbb{S}^n)$.

math.AP↗
arXiv2023

Bulk photovoltaic effect in two-dimensional ferroelectric semiconductor $α$-In$_2$Se$_3$

Bulk photovoltaic effect, which arises from crystal symmetry-driven charge carrier separation, is an intriguing physical phenomenon that has attracted extensive interest in photovoltaic application due to its junction-free photovoltaic and potential to surpass Shockley-Queisser limit. Whereas conventional ferroelectric materials mostly suffer from extremely low photocurrent density and weak photovoltaic response at visible light wavelengths. Emerging two-dimensional ferroelectric semiconductors with coupled visible light absorption and spontaneous polarization characteristics are a promising alternative for making functional photoferroelectrics. Herein, we report the experimental demonstration of the bulk photovoltaic effect behavior based on the 2D ferroelectric semiconductor {$α$-InSe caused by an out-of-plane polarization induced depolarization field. The {$α$-InSe device exhibits enhanced bulk photovoltaic response in the visible light spectrum owing to its narrow bandgap. It was demonstrated that the generated photovoltaic current density was nearly two orders of magnitude greater than conventional bulk ferroelectric materials. These findings highlight the potential of 2D ferroelectric semiconductor materials for bulk photovoltaic applications in a broad spectral region.

cond-mat.mtrl-sci↗
arXiv2023

GaTector: A Unified Framework for Gaze Object Prediction

Gaze object prediction is a newly proposed task that aims to discover the objects being stared at by humans. It is of great application significance but still lacks a unified solution framework. An intuitive solution is to incorporate an object detection branch into an existing gaze prediction method. However, previous gaze prediction methods usually use two different networks to extract features from scene image and head image, which would lead to heavy network architecture and prevent each branch from joint optimization. In this paper, we build a novel framework named GaTector to tackle the gaze object prediction problem in a unified way. Particularly, a specific-general-specific (SGS) feature extractor is firstly proposed to utilize a shared backbone to extract general features for both scene and head images. To better consider the specificity of inputs and tasks, SGS introduces two input-specific blocks before the shared backbone and three task-specific blocks after the shared backbone. Specifically, a novel Defocus layer is designed to generate object-specific features for the object detection task without losing information or requiring extra computations. Moreover, the energy aggregation loss is introduced to guide the gaze heatmap to concentrate on the stared box. In the end, we propose a novel wUoC metric that can reveal the difference between boxes even when they share no overlapping area. Extensive experiments on the GOO dataset verify the superiority of our method in all three tracks, i.e. object detection, gaze estimation, and gaze object prediction.

cs.CV↗
arXiv2021

A Novel Strategy for GaN-on-Diamond Device with a High Thermal Boundary Conductance

To achieve high device performance and high reliability for the gallium nitride (GaN)-based high electron mobility transistors (HEMTs), efficient heat dissipation is important but remains challenging. Enormous efforts have been made to transfer a GaN device layer onto a diamond substrate with a high thermal conductivity by bonding. In this work, two GaN-diamond bonded composites are prepared via modified surface activated bonding (SAB) at room temperature with silicon interlayers of different thicknesses (15 nm and 22 nm). Before and after post-annealing process at 800 oC, thermal boundary conductance (TBC) across the bonded interface including the interlayer and the stress of GaN layer are investigated by time-domain thermoreflectance and Raman spectroscopy, respectively. After bonding, the 15 nm Si interlayer achieved a higher TBC. The post-annealing significantly increased the TBC of both interfaces, while the TBC of 22 nm silicon interlayer increased greater and became higher than that of 15 nm. Detailed investigation of the microstructure and composition of the interfaces were carried out to understand the difference in interfacial thermal conduction. The obtained stress was no more than 230 MPa for both before and after the annealing, and this high thermal stability of the bonded composites indicates that the room temperature bonding can realize a GaN-on-diamond template suitable for further epitaxial growth or device process. This work brings a novel strategy of SAB followed by high-temperature annealing to fabricate a GaN-on-diamond device with a high TBC.

physics.app-ph↗
arXiv2021

A class of Hessian quotient equations in the warped product manifold

In this paper, we consider a class of Hessian quotient equations in the warped product manifold $\overline{M}=I\times_λM$. Under some sufficient conditions, we obtain an existence result for the star-shaped compact hypersurface $Σ$ in $\overline{M}$ using standard degree theory based on a priori estimates for solutions to the Hessian quotient equations.

math.DG↗
arXiv2021

The Dirichlet problem for a class of Hessian quotient equations on Riemannian manifolds

In this paper, we consider the Dirichlet problem for a class of Hessian quotient equations on Riemannian manifolds. Under the assumption of an admissible subsolution, we solve the existence and the uniquness for the Dirichlet problem in a domain without any geometric restrictions on the boundary, based on the a priori estimates for the solutions to the Hessian quotient type equations.

math.AP↗
arXiv2020

A Class of Hessian quotient equations in Euclidean space

In this paper, we consider a Class of Hessian quotient equations in Euclidean space. Under some sufficient condition, we obtain an existence result by the standard degree theory based on the a prior estimates for the solutions to the Hessian quotient equations.

math.AP↗