Reflection of Willmore Surfaces with Free Boundaries
-
Published:2020-03-11
Issue:
Volume:
Page:1-18
-
ISSN:0008-414X
-
Container-title:Canadian Journal of Mathematics
-
language:en
-
Short-container-title:Can. J. Math.-J. Can. Math.
Author:
Kuwert Ernst,Lamm Tobias
Abstract
Abstract
We study immersed surfaces in
${\mathbb R}^3$
that are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary and when the boundary is contained in a line. In both cases we derive weak forms of the resulting free boundary conditions and prove regularity by reflection.
Publisher
Canadian Mathematical Society
Subject
General Mathematics