Rigidity theorem for Willmore surfaces in a sphere

被引：0

作者：

HONGWEI XU

DENGYUN YANG

机构：

[1] Zhejiang University,Center of Mathematical Sciences

[2] Jiangxi Normal University,College of Mathematics and Information Science

来源：

Proceedings - Mathematical Sciences | 2016年 / 126卷

关键词：

Willmore functional; Sobolev inequality; mean curvature; totally umbilical surface; 53C40; 53C24;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let M2 be a compact Willmore surface in the (2 + p)-dimensional unit sphere S2 + p. Denote by H and S the mean curvature and the squared length of the second fundamental form of M2, respectively. Set ρ2 = S−2H2. In this note, we proved that there exists a universal positive constant C, such that if ∥ρ2∥2<C, then ρ2=0 and M2 is a totally umbilical sphere.

引用

页码：253 / 260

页数：7

共 50 条

[1] Rigidity theorem for Willmore surfaces in a sphere
Xu, Hongwei
Yang, Dengyun
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2016, 126 (02): : 253 - 260
[2] A PINCHING THEOREM FOR CONFORMAL CLASSES OF WILLMORE SURFACES IN THE UNIT n-SPHERE
Chang, Yu-Chung
Hsu, Yi-Jung
BULLETIN OF THE INSTITUTE OF MATHEMATICS ACADEMIA SINICA NEW SERIES, 2006, 1 (02): : 231 - 261
[3] A DUALITY THEOREM FOR WILLMORE SURFACES
BRYANT, RL
JOURNAL OF DIFFERENTIAL GEOMETRY, 1984, 20 (01) : 23 - 53
[4] Rigidity of Willmore submanifolds and extremal submanifolds in the unit sphere
Deng-Yun Yang
Hai-Ping Fu
Jin-Guo Zhang
Archiv der Mathematik, 2023, 121 : 329 - 342
[5] Willmore Surfaces of ℝ4 and the Whitney Sphere
Ildefonso Castro
Francisco Urbano
Annals of Global Analysis and Geometry, 2001, 19 : 153 - 175
[6] Rigidity of Willmore submanifolds and extremal submanifolds in the unit sphere
Yang, Deng-Yun
Fu, Hai-Ping
Zhang, Jin-Guo
ARCHIV DER MATHEMATIK, 2023, 121 (03) : 329 - 342
[7] On the Second Pinching Theorem for Willmore Hypersurfaces in a Sphere
Li, Haizhong
Zhang, Meng
RESULTS IN MATHEMATICS, 2024, 79 (03)
[8] On the Second Pinching Theorem for Willmore Hypersurfaces in a Sphere
Haizhong Li
Meng Zhang
Results in Mathematics, 2024, 79
[9] A rigidity theorem for hypersurfaces in a sphere
Liu, XM
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2002, 60 (1-2): : 107 - 114
[10] Willmore surfaces in the unit N-sphere
Chang, YC
Hsu, YJ
TAIWANESE JOURNAL OF MATHEMATICS, 2004, 8 (03): : 467 - 476

← 1 2 3 4 5 →