Nonnegatively curved hypersurfaces with free boundary on a sphere

被引：3

作者：

Ghomi, Mohammad ^{[1
]}

Xiong, Changwei ^{[2
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Australian Natl Univ, Inst Math Sci, Canberra, ACT 2601, Australia

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2019年 / 58卷 / 03期

关键词：

CONSTANT MEAN-CURVATURE; CONVEX; SYMMETRY;

D O I：

10.1007/s00526-019-1532-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that in Euclidean space Rn+1 any compact immersed nonnegatively curved hypersurface M with free boundary on the sphere Sn is an embedded convex topological disk. In particular, when the mth mean curvature of M is constant, for any 1mn, M is a spherical cap or an equatorial disk.

引用

页数：20

共 43 条

[11] do Carmo MP., 1970, J DIFFERENTIAL GEOME, V4, P133
[12] ISOMETRIC IMMERSIONS WITH SEMI-DEFINITE SECOND QUADRATIC FORMS
DOCARMO, MP
LIMA, E
[J]. ARCHIV DER MATHEMATIK, 1969, 20 (02) : 173 - &
[13] Federer H., 2014, GEOMETRIC MEASURE TH
[14] The first Steklov eigenvalue, conformal geometry, and minimal surfaces
Fraser, Ailana
Schoen, Richard
[J]. ADVANCES IN MATHEMATICS, 2011, 226 (05) : 4011 - 4030
[15] Shadows and convexity of surfaces
Ghomi, M
[J]. ANNALS OF MATHEMATICS, 2002, 155 (01) : 281 - 293
[16] Ghomi M, 2001, J DIFFER GEOM, V57, P239
[17] Ghomi M, 2017, J DIFFER GEOM, V105, P427
[18] Tangent cones and regularity of real hypersurfaces
Ghomi, Mohammad
Howard, Ralph
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2014, 697 : 221 - 247
[19] TANGENT LINES, INFLECTIONS, AND VERTICES OF CLOSED CURVES
Ghomi, Mohammad
[J]. DUKE MATHEMATICAL JOURNAL, 2013, 162 (14) : 2691 - 2730
[20] Hadamard J, 1897, CERTAINES PROPRIETES

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