On stability of capillary surfaces in a ball

被引：95

作者：

Ros, A ^{[1
]}

Souam, R ^{[1
]}

机构：

[1] UNIV PARIS 07, CNRS UMR GEOMETRIE & DYNAM C9994, F-75251 PARIS 05, FRANCE

来源：

PACIFIC JOURNAL OF MATHEMATICS | 1997年 / 178卷 / 02期

关键词：

D O I：

10.2140/pjm.1997.178.345

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study stable capillary surfaces in a euclidean ball in the absence of gravity. We prove, in particular, that such a surface must be a flat disk or a spherical cap if it has genus zero. We also prove that its genus is at most one and it has at most three connected boundary components in case it is minimal. Some of our results also hold in H-3 and S-3.

引用

页码：345 / 361

页数：17

共 18 条

[1] STABILITY OF HYPERSURFACES OF CONSTANT MEAN-CURVATURE IN RIEMANNIAN-MANIFOLDS [J].

BARBOSA, JL ;

DOCARMO, M ;

ESCHENBURG, J .

MATHEMATISCHE ZEITSCHRIFT, 1988, 197 (01) :123-138

[2] EIGENFUNCTIONS AND NODAL SETS [J].

CHENG, SY .

COMMENTARII MATHEMATICI HELVETICI, 1976, 51 (01) :43-55

[3]

CHERN SS, 1989, SURFACES CONSTANT ME

[4] INCREASE IN THE 2ND EIGENVALUE OF A SCHRODINGER OPERATOR ON A COMPACT MANIFOLD AND APPLICATIONS [J].

ELSOUFI, A ;

ILIAS, S .

JOURNAL OF FUNCTIONAL ANALYSIS, 1992, 103 (02) :294-316

[5]

Finn R., 1986, EQUILIBRIUM CAPILLAR

[6] EXISTENCE AND REGULARITY FOR THE PROBLEM OF A PENDENT LIQUID-DROP [J].

GONZALEZ, E ;

MASSARI, U ;

TAMANINI, I .

PACIFIC JOURNAL OF MATHEMATICS, 1980, 88 (02) :399-420

[7]

Griffiths P., 1994, PRINCIPLES ALGEBRAIC

[8]

HERSCH J, 1970, CR ACAD SCI A MATH, V270, P1645

[9] A NEW CONFORMAL INVARIANT AND ITS APPLICATIONS TO THE WILLMORE CONJECTURE AND THE 1ST EIGENVALUE OF COMPACT SURFACES [J].

LI, P ;

YAU, ST .

INVENTIONES MATHEMATICAE, 1982, 69 (02) :269-291

[10] STATIONARY PARTITIONING OF CONVEX-BODIES [J].

NITSCHE, JCC .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1985, 89 (01) :1-19

← 1 2 →