Rigidity Result for Four Dimensional Willmore Submanifolds with Boundary
Differential Geometry
2023-05-18 v1 Analysis of PDEs
Abstract
We establish a rigidity result for the critical points, with boundary, of a four dimensional Willmore energy. These critical points satisfy a 4-Willmore equation which is a sixth order nonlinear elliptic partial differential equation. We establish several curvature estimates and prove that four dimensional Willmore submanifold with totally geodesic boundary condition are umbilic.
Cite
@article{arxiv.2305.09854,
title = {Rigidity Result for Four Dimensional Willmore Submanifolds with Boundary},
author = {Peter Olamide Olanipekun},
journal= {arXiv preprint arXiv:2305.09854},
year = {2023}
}