Skip to main content
placeholder image

A rigidity theorem for ideal surfaces with flat boundary

Journal Article


Download full-text (Open Access)

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.

Publication Date


  • 2019

Citation


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

Scopus Eid


  • 2-s2.0-85072127961

Ro Full-text Url


  • https://ro.uow.edu.au/cgi/viewcontent.cgi?article=4210&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/3191

Number Of Pages


  • 12

Start Page


  • 1

End Page


  • 13

Volume


  • Online First

Place Of Publication


  • Netherlands

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.

Publication Date


  • 2019

Citation


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

Scopus Eid


  • 2-s2.0-85072127961

Ro Full-text Url


  • https://ro.uow.edu.au/cgi/viewcontent.cgi?article=4210&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/3191

Number Of Pages


  • 12

Start Page


  • 1

End Page


  • 13

Volume


  • Online First

Place Of Publication


  • Netherlands