AN AREA BOUND FOR SURFACES IN RIEMANNIAN MANIFOLDS

被引：0

作者：

Bangert, Victor ^{[1
]}

Kuwert, Ernst ^{[1
]}

机构：

[1] Albert Ludwigs Univ Freiburg, Math Inst, Ernst Zermelo Str 1, D-79104 Freiburg, Germany

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2025年 / 129卷 / 01期

关键词：

COMPACTNESS THEOREM; IMMERSIONS; EXISTENCE; CURVATURE; SPHERES;

D O I：

10.4310/jdg/1736261979

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let M be a compact Riemannian manifold not containing any totally geodesic surface. Our main result shows that then the area of any complete surface immersed into M is bounded by a multiple of its extrinsic curvature energy, i.e. by a multiple of the integral of the squared norm of its second fundamental form.

引用

页码：65 / 113

页数：49

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