Work

Rigidity and nonexistence of CMC spacelike hypersurfaces via an Okumura type inequality in a class of Lorentzian Einstein manifolds

Year: 2026

Type: article

Abstract: Our purpose is to investigate geometric aspects of complete and stochastically complete CMC spacelike hypersurfaces immersed into a class of Lorentzian Einstein manifolds satisfying appropriate curvature constraints. Assuming that the total umbilicity tensor satisfies an Okumura type inequality, we derive a suitable Simons type inequality which, jointly with several maximum principles and certain integrability conditions, enable us to establish rigidity and nonexistence results concerning these spacelike hypersurfaces.

Source: manuscripta mathematica

DOI: 10.1007/s00229-026-01697-4

Authors: Henrique F. de Lima, Ary V. F. Leite, Marco A. L. Velásquez

Institution: Universidade Federal de Campina Grande

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico