Uniqueness of free boundary minimal hypersurfaces in rotational domains

被引：2

作者：

Barbosa, Ezequiel ^{[1
]}

Freitas, Allan ^{[2
]}

Melo, Rodrigo ^{[3
]}

Vitorio, Feliciano ^{[4
]}

机构：

[1] Univ Fed Minas Gerais, Inst Ciencias Exatas, BR-30161970 Belo Horizonte, MG, Brazil

[2] Univ Fed Paraiba, Dept Matemat, BR-58059900 Joao Pessoa, Paraiba, Brazil

[3] Univ Fed Alagoas, Campus Sertao,Rodovia AL 145, BR-57480000 Delmiro Gouveia, Alagoas, Brazil

[4] Univ Fed Alagoas, Inst Matemat, Campus AC Simoes,BR 104-Norte,Km 97, BR-57072970 Maceio, Alagoas, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 525卷 / 02期

关键词：

Free boundary; Minimal surfaces; CAPILLARY SURFACES; MEAN-CURVATURE; SPACE;

D O I：

10.1016/j.jmaa.2023.127172

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we investigate the existence of compact free boundary minimal hypersurfaces immersed in several domains. Using an original integral identity for compact free boundary minimal hypersurfaces that are immersed in a domain whose boundary is a regular level set, we study the case where this domain is a quadric or, more generally, a rotational domain. This existence study is done without topological restrictions. We also obtain a new gap theorem for free boundary hypersurfaces immersed in an Euclidean ball and in a rotational ellipsoid.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：20

共 28 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]

Ambrozio L, 2021, COMMUN ANAL GEOM, V29, P283

[3] Uniqueness Results for Free Boundary Minimal Hypersurfaces in Conformally Euclidean Balls and Annular Domains [J].

Barbosa, Ezequiel ;

Goncalves, Rosivaldo Antonio ;

Pereira, Edno .

JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (10) :9800-9818

[4] A remark on a curvature gap for minimal surfaces in the ball [J].

Barbosa, Ezequiel ;

Viana, Celso .

MATHEMATISCHE ZEITSCHRIFT, 2020, 294 (1-2) :713-720

[5]

Bjorling E.G., 1844, ARCH MATH PHYS, V4, P290

[6] Vanishing theorems for the cohomology groups of free boundary submanifolds [J].

Cavalcante, Marcos P. ;

Mendes, Abraao ;

Vitorio, Feliciano .

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2019, 56 (01) :137-146

[7] Capillary surfaces in a convex cone [J].

Choe, Jaigyoung ;

Park, Sung-Ho .

MATHEMATISCHE ZEITSCHRIFT, 2011, 267 (3-4) :875-886

[8] The existence of minimal surfaces of given topological structure under prescribed boundary conditions [J].

Courant, R .

ACTA MATHEMATICA, 1940, 72 (01) :51-98

[9] Solution of the problem of plateau [J].

Douglas, Jesse .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1931, 33 (1-4) :263-321

[10]

Evans LC., 2010, Partial Differential Equations, V2

← 1 2 3 →