Hypersurfaces in Spheres with Finite Total Curvature

被引：3

作者：

Zhu, Peng ^{[1
]}

机构：

[1] Jiangsu Univ Technol, Sch Math & Phys, Changzhou 213001, Jiangsu, Peoples R China

来源：

RESULTS IN MATHEMATICS | 2019年 / 74卷 / 04期

关键词：

Reduced L-2 cohomology; hypersurfaces in spheres; total curvature; MINIMAL-SURFACES; SUBMANIFOLDS; COHOMOLOGY;

D O I：

10.1007/s00025-019-1082-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Suppose that M is a complete noncompact hypersurface in a sphere Sn+1 (n >= 3) with finite total curvature. We show that each p-th space of reduced L-2-cohomology on M has finite dimension, for 0 <= p <= n. This result solves the conjecture posed in Zhu (Ann Braz Acad Sci 88: 2053-2065, 2016).

引用

页数：13

共 50 条

[1] Hypersurfaces in Spheres with Finite Total Curvature
Peng Zhu
[J]. Results in Mathematics, 2019, 74
[2] On reduced L2 cohomology of hypersurfaces in spheres with finite total curvature
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[J]. ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS, 2016, 88 (04): : 2053 - 2065
[3] HYPERSURFACES IN EUCLIDEAN SPACES WITH FINITE TOTAL CURVATURE
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[4] On the compactness of constant mean curvature hypersurfaces with finite total curvature
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[5] Complete hypersurfaces with constant mean curvature and finite total curvature
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