Second boundary value problem for the Hessian curvature flow
Analysis of PDEs
2025-05-30 v1
Abstract
We investigate the evolution of strictly convex hypersurfaces driven by the -Hessian curvature flow, subject to the second boundary condition. We first explore the translating solutions corresponding to this boundary value problem. Next, we establish the long-time existence of the flow and prove that it converges to a translating solution. To overcome the difficulty of driving boundary estimates, we employ an orthogonal invariance technique. Using this method, we extend the results of Schn\"urer-Smoczyk \cite{Schnurer2003} and Schn\"urer \cite{Schnurer2002} from the second boundary value problem of Gauss curvature flow to -Hessian curvature flow.
Cite
@article{arxiv.2505.23067,
title = {Second boundary value problem for the Hessian curvature flow},
author = {Rongli Huang and Changzheng Qu and Zhizhang Wang and Weifeng Wo},
journal= {arXiv preprint arXiv:2505.23067},
year = {2025}
}