Contraction of convex hypersurfaces by nonhomogeneous functions of curvature

A Pinching Estimate for Convex Hypersurfaces Evolving Under a Nonhomogeneous Variant of Mean Curvature Flow

We study a variant of the mean curvature flow for closed, convex hypersurfaces where the normal velocity is a nonhomogeneous function of the principal curvatures. We show that if the initial hypersurface satisfies a certain pinching condition, then this is preserved and the flow converges to a sphere under rescaling.

运动超曲面上的随机Stefan问题：基于非齐次单调性新框架的方法

Stochastic Stefan problem on moving hypersurfaces: an approach by a new framework of nonhomogeneous monotonicity

本文通过设计特殊变换，利用涉及时间依赖算子的非齐次单调性新框架，建立了运动超曲面上随机Stefan问题的适定性，并推广至求解其他随机偏微分方程模型。

Contracting self-similar solutions of nonhomogeneous curvature flows

A recent article by Li and Lv considered fully nonlinear contraction of convex hypersurfaces by certain nonhomogeneous functions of curvature, showing convergence to points in finite time in cases where the speed is a function of a degree-one homogeneous, concave and inverse concave function of the principle curvatures. In this article we consider self-similar solutions to these and related curvature flows that are not homogeneous in the principle curvatures, finding various situations where closed, convex curvature-pinched hypersurfaces contracting self-similarly are necessarily spheres.

一类 Hessian 曲率方程的 k - 凸超曲面的存在性

The existence of $k$-convex hypersurface for a class of Hessian curvature equations

研究一类 Hessian 曲率方程闭星形超曲面存在性，结合先验估计与连续性方法建立 k - 凸超曲面存在唯一性，通过常秩定理证其严格凸。

$\mathbb R^3$ 中凸超曲面由主曲率幂的收缩

Contraction of Convex Hypersurfaces in $\mathbb R^3$ by Powers of Principal Curvatures

本文研究了严格凸的轴对称超曲面在非对称、非齐次完全非线性曲率函数作用下的收缩问题，证明了其在有限时间内收敛至一点，且经适当缩放后解收敛至凸超曲面。

双曲空间中保体积的非齐次高斯曲率流

Volume preserving nonhomogeneous Gauss curvature flow in hyperbolic space

研究双曲空间中保体积非齐次高斯曲率流，证明解在所有正时间存在且指数收敛到测地球，关键在于高斯曲率振荡衰减与双曲曲率测度论结合推导出 Hausdorff 收敛。