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arXiv · 2305.09854

Rigidity Result for Four Dimensional Willmore Submanifolds with Boundary

Peter Olamide Olanipekun
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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.

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Peter Olamide Olanipekun. 2023-05-16. Rigidity Result for Four Dimensional Willmore Submanifolds with Boundary. https://arxiv.org/abs/2305.09854

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