Nonexistence and rigidity of spacelike mean curvature flow solitons immersed in a GRW spacetime

被引：2
作者：
Freitas, Allan [1 ]
de Lima, Henrique F. [2 ]
Santos, Marcio S. [1 ]
Sindeaux, Joyce S. [1 ]
机构：
[1] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil
[2] Univ Fed Campina Grande, Dept Matemat, BR-58429970 Campina Grande, Paraiba, Brazil
来源：
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2023年 / 63卷 / 01期
关键词：
Generalized Robertson-Walker spacetimes; Spacelike mean curvature flow solitons; Trapped submanifolds; Higher-order mean curvatures; GRAVITATIONAL COLLAPSE; TRAPPED SURFACES; 1ST EIGENVALUE; HYPERSURFACES; SUBMANIFOLDS; UNIQUENESS; LAPLACIAN; GRAPHS;
D O I：
10.1007/s10455-022-09879-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the nonexistence and rigidity of an important class of particular cases of trapped submanifolds, more precisely, n-dimensional spacelike mean curvature flow solitons related to the closed conformal timelike vector field K = f (t) partial derivative(t) (t is an element of I subset of R) which is globally defined on an (n + p + 1)-dimensional generalized Robertson-Walker (GRW) spacetime -I x(f) Mn+p with warping function f is an element of C-infinity (I) and Riemannian fiber Mn+p, via applications of suitable generalized maximum principles and under certain constraints on f and on the curvatures of Mn+p. In codimension 1, we also obtain new Calabi-Bernstein-type results concerning the spacelike mean curvature flow soliton equation in a GRW spacetime.
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页数：35
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