English

A rigidity theorem for ideal surfaces with flat boundary

Differential Geometry 2018-12-13 v1

Abstract

We consider surfaces with boundary satisfying a sixth order nonlinear elliptic partial differential equation corresponding to extremising the L2L^2-norm of the gradient of the mean curvature. We show that such surfaces with small L2L^2-norm of the second fundamental form and satisfying so-called `flat boundary conditions' are necessarily planar.

Keywords

Cite

@article{arxiv.1812.04761,
  title  = {A rigidity theorem for ideal surfaces with flat boundary},
  author = {James McCoy and Glen Wheeler},
  journal= {arXiv preprint arXiv:1812.04761},
  year   = {2018}
}

Comments

12 pages

R2 v1 2026-06-23T06:39:44.070Z