Ends of immersed minimal and Willmore surfaces in asymptotically at spaces

Yann Bernard, Tristan Riviére

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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 at spaces of any dimension; assuming the surface has L2-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 in any codimension.

Original languageEnglish
Pages (from-to)1-57
Number of pages57
JournalCommunications in Analysis and Geometry
Issue number1
Publication statusPublished - 1 Jan 2020

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