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.