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A rigidity theorem for ideal surfaces with flat boundary

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posted on 2024-11-16, 03:55 authored by James McCoyJames McCoy, Glen WheelerGlen Wheeler
We consider surfaces with boundary satisfying a sixth-order nonlinear elliptic partial differential equation corresponding to extremising the L2-norm of the gradient of the mean curvature. We show that such surfaces with small L2-norm of the second fundamental form and satisfying so-called flat boundary conditions are necessarily planar.

Funding

Higher order curvature flow of curves and hypersurfaces

Australian Research Council

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Parabolic methods for elliptic boundary value problems

Australian Research Council

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History

Citation

McCoy, J. & Wheeler, G. (2019). A rigidity theorem for ideal surfaces with flat boundary. Annals of Global Analysis and Geometry, Online First 1-13.

Journal title

Annals of Global Analysis and Geometry

Volume

57

Issue

1

Pagination

1-13

Language

English

RIS ID

138764

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