A rigidity theorem for ideal surfaces with flat boundary

Authors

James A. McCoy, University of NewcastleFollow
Glen Wheeler, University of WollongongFollow

RIS ID

138764

Publication Details

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

Abstract

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.

Grant Number

ARC/DP150100375

Grant Number

ARC/DP180100431