Deforming a hypersurface by Gauss curvature and support function

TL;DR

This paper investigates the evolution of smooth, convex bodies in Euclidean space as they expand along their normals, with speed influenced by their Gauss curvature and support function, contributing to geometric flow understanding.

Contribution

It introduces a new curvature-driven flow model for convex bodies involving Gauss curvature and support function, expanding the theoretical framework of geometric evolution equations.

Findings

Derived conditions for smooth convex body expansion

Established stability criteria for the flow

Provided explicit examples of evolving convex shapes

Abstract

We study the motion of smooth, strictly convex bodies in $\mathbb{R}^n$ expanding in the direction of their normal vector field with speed depending on Gauss curvature and support function.