Evolution of starshaped hypersurfaces by general curvature functions

TL;DR

This paper studies how starshaped hypersurfaces evolve in Euclidean space under general curvature functions, proving they exist globally and converge to a shape with prescribed curvature.

Contribution

It establishes conditions under which the evolution flow exists globally and converges, extending previous results to more general curvature functions.

Findings

Flow exists globally under certain curvature conditions.

Hypersurfaces converge to prescribed curvature shapes.

Results generalize previous curvature flow theories.

Abstract

We consider the evolution of starshaped hypersurfaces in the Euclidean space by general curvature functions. Under appropriate conditions on the curvature function, we prove the global existence and convergence of the flow to a hypersurface of prescribed curvature.