Neumann boundary value problem for gernera curvature flow with forcing term

TL;DR

This paper establishes long-term existence and convergence for a class of curvature flows with Neumann boundary conditions, pioneering results for non-Monge-Ampère type equations and applicable to elliptic problems.

Contribution

It provides the first proof of long-time existence and convergence for Neumann boundary problems in non-Monge-Ampère curvature flows, extending to elliptic cases.

Findings

Proved long-time existence of solutions.

Established convergence of the curvature flow.

Extended results to elliptic equations.

Abstract

In this paper, we prove long time existence and convergence results for a class of general curvature flows with Neumann boundary condition. This is the first result for the Neumann boundary problem of non Monge-Ampere type curvature equations. Our method also works for the corresponding elliptic setting.