General curvature flow without singularities

TL;DR

This paper extends the study of mean curvature flow to a broader class of curvature flows, establishing long-term existence results and new interpretations of weak flows without encountering singularities.

Contribution

It generalizes previous results on graphical mean curvature flow to a wider curvature setting, including boundary conditions and singularity-free evolution.

Findings

Proved long-time existence of general curvature flows

Provided a new interpretation of weak curvature flows

Established existence results with boundary conditions

Abstract

In [5], S\'aez and Schn\"urer studied the graphical mean curvature flow of complete hypersurfaces defined on subsets of Euclidean space. They obtained long time existence. Moreover, they provided a new interpretation of weak mean curvature flow. In this paper, we generalize their results to a general curvature setting. Our key ingredient is the existence result of general curvature flow with boundary conditions, which is proved in Section 4.