Stability of Capillary Hypersurfaces with Constant Higher Order Mean Curvature

被引:0
作者
Damasceno, Leonardo [1 ]
Elbert, Maria Fernanda [2 ]
机构
[1] Univ Estado Rio De Janeiro, Inst Matemat & Estat, Rio De Janeiro, RJ, Brazil
[2] Univ Fed Rio De Janeiro, Inst Matemat, Rio De Janeiro, RJ, Brazil
关键词
Isometric immersions; Free boundary; Capillary; Higher order mean curvature; FREE-BOUNDARY; SPACE; SURFACES;
D O I
10.1007/s12220-024-01831-2
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We propose a notion of stability for capillary hypersurfaces with constant higher order mean curvature and we generalize some results of the classical stability theory for constant mean curvature capillary hypersurfaces.
引用
收藏
页数:37
相关论文
共 30 条
[1]   Stable Capillary Hypersurfaces in a Half-Space or a Slab [J].
Ainouz, Abdelhamid ;
Souam, Rabah .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2016, 65 (03) :813-831
[2]   Stable surfaces and free boundary marginally outer trapped surfaces [J].
Alaee, Aghil ;
Lesourd, Martin ;
Yau, Shing-Tung .
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (05)
[3]   Integral formulas for the r-mean curvature linearized operator of a hypersurface [J].
Alencar, H ;
Colares, AG .
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 1998, 16 (03) :203-220
[4]   STABILITY OF HYPERSURFACES OF CONSTANT MEAN-CURVATURE IN RIEMANNIAN-MANIFOLDS [J].
BARBOSA, JL ;
DOCARMO, M ;
ESCHENBURG, J .
MATHEMATISCHE ZEITSCHRIFT, 1988, 197 (01) :123-138
[5]   STABILITY OF HYPERSURFACES WITH CONSTANT MEAN-CURVATURE [J].
BARBOSA, JL ;
DOCARMO, M .
MATHEMATISCHE ZEITSCHRIFT, 1984, 185 (03) :339-353
[6]  
Barbosa JLM, 1997, ANN GLOB ANAL GEOM, V15, P277
[7]  
Chavel I., 1984, EIGENVALUES RIEMANNI
[8]   Embedded positive constant r-mean curvature hypersurfaces in Mm x R [J].
Cheng, X ;
Rosenberg, H .
ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS, 2005, 77 (02) :183-199
[9]   STABLE CAPILLARY HYPERSURFACES IN A WEDGE [J].
Choe, Jaigyoung ;
Koiso, Miyuki .
PACIFIC JOURNAL OF MATHEMATICS, 2016, 280 (01) :1-15
[10]   On the stability of constant higher order mean curvature hypersurfaces in a Riemannian manifold [J].
Elbert, Maria Fernanda ;
Nelli, Barbara .
MATHEMATISCHE NACHRICHTEN, 2024, 297 (11) :4031-4043