A curvature flow approach to Lp-Christoffel-Minkowski problem for p>1
Li Chen, Qiang Tu, Ni Xiang
TL;DR
This paper introduces a curvature flow method to address the Lp-Christoffel-Minkowski problem for p>1, providing a unified approach to solving this geometric problem involving convex hypersurfaces.
Contribution
It develops a curvature flow technique to solve the Lp-Christoffel-Minkowski problem for p>1, advancing the understanding of convex hypersurface evolution.
Findings
Established a curvature flow approach for p>1
Provided convergence results for the flow
Unified the solution framework for the Lp-Christoffel-Minkowski problem
Abstract
We study the motion of smooth, closed, strictly convex hypersurfaces in Rn+1 expanding in the direction of their normal vector field with speed depending on the k-th elementary symmetric polynomial of the principal radii of curvature. As an application, we gives a unifed fow approach to Lp-Christoffel-Minkowski problem for p > 1.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Point processes and geometric inequalities