TY - JOUR
T1 - Ends of immersed minimal and Willmore surfaces in asymptotically at spaces
AU - Bernard, Yann
AU - Riviére, Tristan
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85086381773&partnerID=8YFLogxK
U2 - 10.4310/CAG.2020.V28.N1.A1
DO - 10.4310/CAG.2020.V28.N1.A1
M3 - Article
AN - SCOPUS:85086381773
SN - 1019-8385
VL - 28
SP - 1
EP - 57
JO - Communications in Analysis and Geometry
JF - Communications in Analysis and Geometry
IS - 1
ER -