Flow by powers of the Gauss curvature in space formsEntropyGauss curvatureMonotonicityRegularity estimatesSpace formsCONVEX HYPERSURFACESCONTRACTIONSURFACESENTROPYSHAPESIn this paper, we prove that convex hypersurfaces under the flow by powers alpha > 0 of the Gauss curvature in space forms Nn+1 (K) ...
In this talk, I will introduce our recent work on Gauss curvature flow with Xu-Jia Wang and Qi-Rui Li. In this work we study a contracting flow of closed, convex hypersurfaces in the Euclidean space $\R^{n+1}$ with the speed $f r^{\alpha} K$, where $K$ is the Gauss curvature...
CURVATUREWe consider a flow by powers of Gauss curvature under the obstruction that the flow cannot penetrate a prescribed region, so called an obstacle. For all dimensions and positive powers, we prove the optimal curvature bounds of solutions and all time existence with its long time behavior....
The speed equals a powerβ(≥1)of homogeneous curvature functions of degree one and either convex or concave plus a mixed volume preserving term, including the case of powers of the mean curvature and of the Gauss curvature. The main result is that if the initial hypersurface satisfies a ...
This problem comes from the study of Gauss curvature flow and its generalization, the flow by powers of Gauss curvature.doi:10.1016/j.na.2012.01.020Hongjie JuJiguang BaoHuaiyu JianNonlinear AnalysisH. Ju, J. Bao, and H. Jian, "Existence for translating solutions of Gauss curvature flow on ...
SMOOTHNESS of functionsMINKOWSKI spaceSTOCHASTIC convergenceIn this paper we study a contracting flow of closed, convex hypersurfaces in the Euclidean space Rn 1 with speed frαK, where K is the Gauss curvature, r is the distance from the hypersurface to the origin, and f is a...
Gauss curvature flowChord integralLφdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$L_varphi $$end{document} chord measures...
In this paper, we study the $ L_p $ dual Minkowski problem, an extension of the dual Minkowski problem. We deal with some cases in which there is no uniform estimate for the Gauss curvature flow. We adopt the topological method from [13] to find a special initial condition such that ...
Flow by Gauss curvature to the Aleksandrov and dual Minkowski problemsdoi:10.4171/JEMS/936Qi-Rui LiWeimin ShengXu-Jia WangEuropean Mathematical Society Publishing House
On a crystalline Gauss curvature flowTakeo K. Ushijima