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A rigidity theorem for ideal surfaces with flat boundary

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journal contribution
posted on 2025-05-09, 16:48 authored by James McCoyJames McCoy, Glen 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

ARC

DP150100375

180100431

History

Journal title

Annals of Global Analysis and Geometry

Volume

57

Pagination

1-13

Publisher

Springer Netherlands

Place published

Dordrecht, Netherlands

Language

  • en, English

College/Research Centre

Faculty of Science

School

Centre for Computer Assisted Research Mathematics and its Applications (CARMA)

Rights statement

This is a post-peer-review, pre-copyedit version of an article published in the Annals of Global Analysis and Geometry. The final authenticated version is available online at: http://doi.org/10.1007/s10455-019-09685-6.