Solitons of the spacelike mean curvature flow in generalized Robertson-Walker spacetimes

被引：0

作者：

Batista, Marcio ^{[1
]}

Bisci, Giovanni Molica ^{[2
]}

Lima, Henrique F. de ^{[3
]}

Gomes, Wallace F. ^{[3
]}

机构：

[1] Univ Fed Alagoas, CPMAT IM, BR-57072970 Maceio, AL, Brazil

[2] Univ Studi Urbino Carlo Bo, Dipartimento Sci Pure & Applicate DISPEA, Piazza Repubbl 13, I-61029 Urbino, Italy

[3] Univ Fed Campina Grande, Dept Matemat, 58, BR-42997 Campina Grande, PB, Brazil

来源：

NEW YORK JOURNAL OF MATHEMATICS | 2023年 / 29卷

关键词：

Generalized Robertson-Walker spacetime; complete spacelike mean curvature flow solitons; Einstein-de Sitter spacetime; steady state type spacetimes; de Sitter and anti-de Sitter spaces; Calabi-Bernstein type results; TRANSLATING SOLITONS; HYPERSURFACES; UNIQUENESS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Our purpose in this paper is to study solitons of the spacelike mean curvature flow in a generalized Robertson-Walker (GRW) spacetime -I x(f )M(n). Under suitable constraints on the warping function f and on the curvatures of the Riemannian fiber M-n, we apply suitable maximum princi-ples in order to obtain nonexistence and uniqueness results concerning these solitons. Applications to standard models of GRW spacetimes, namely, the Einstein-de Sitter spacetime, steady state type spacetimes, de Sitter and anti -de Sitter spaces, are given. Furthermore, we establish new Calabi-Bernstein type results related to entire spacelike mean curvature flow graphs constructed over the Riemannian fiber of the ambient spacetime.

引用

页码：554 / 579

页数：26

共 42 条

[1] Mean curvature flow with a forcing term in Minkowski space [J].

Aarons, MAS .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2006, 25 (02) :205-246

[2]

Ahlfors L. V., 1935, C.R. Acad. Sci. Paris, V201, P30

[3]

Albujer AL, 2009, P AM MATH SOC, V137, P711

[4] New examples of entire maximal graphs in H2 x R1 [J].

Albujer, Alma L. .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2008, 26 (04) :456-462

[5] Integral formulas for compact space-like hypersurfaces in de Sitter space:: Applications to the case of constant higher order mean curvature [J].

Aledo, JA ;

Alías, LJ ;

Romero, A .

JOURNAL OF GEOMETRY AND PHYSICS, 1999, 31 (2-3) :195-208

[6] Space-like hypersurfaces with functionally bounded mean curvature in Lorentzian warped products and generalized Calabi-Bernstein-type problems [J].

Aledo, Juan A. ;

Rubio, Rafael M. ;

Salamanca, Juan J. .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2019, 149 (04) :849-868

[7] UNIQUENESS OF COMPLETE SPACELIKE HYPERSURFACES OF CONSTANT MEAN-CURVATURE IN GENERALIZED ROBERTSON-WALKER SPACETIMES [J].

ALIAS, LJ ;

ROMERO, A ;

SANCHEZ, M .

GENERAL RELATIVITY AND GRAVITATION, 1995, 27 (01) :71-84

[8]

Alias LJ., 2016, Maximum Principles and Geometric Applications, DOI [10.1007/978-3-319-24337-5, DOI 10.1007/978-3-319-24337-5]

[9] Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes [J].

Alias, Luis J. ;

Colares, A. Gervasio .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2007, 143 :703-729

[10] Mean Curvature Flow Solitons in the Presence of Conformal Vector Fields [J].

Alias, Luis J. ;

de Lira, Jorge H. ;

Rigoli, Marco .

JOURNAL OF GEOMETRIC ANALYSIS, 2020, 30 (02) :1466-1529

← 1 2 3 4 5 →