Ends of Immersed Minimal and Willmore Surfaces in Asymptotically Flat Spaces
Differential Geometry
2016-03-29 v2
Abstract
We study ends of an oriented, immersed, non-compact, complete Willmore surfaces, which are critical points of the integral of the square of the mean curvature, in asymptotically flat spaces of any dimension; assuming the surface has -bounded second fundamental form and satisfies a weak power growth on the area. We give the precise asymptotic behavior of an end of such a surface. This asymptotic information is very much dependent on the way the ambient metric decays to the Euclidean one. Our results apply in particular to minimal surfaces.
Keywords
Cite
@article{arxiv.1508.01391,
title = {Ends of Immersed Minimal and Willmore Surfaces in Asymptotically Flat Spaces},
author = {Yann Bernard and Tristan Riviere},
journal= {arXiv preprint arXiv:1508.01391},
year = {2016}
}
Comments
This second version corrects typos from the previous one and includes a more general hypothesis on the growth of the area of the complete surface