Ends of Immersed Minimal and Willmore Surfaces in Asymptotically Flat Spaces

Autor:	Bernard, Yann, Riviere, Tristan
Rok vydání:	2015
Předmět:	Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	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 $L^2$-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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1508.01391 Zobrazit plný text záznamu View this record from Arxiv