Umbilicity and the First Stability Eigenvalue of a Subclass of CMC Hypersurfaces Immersed in Certain Einstein Manifolds

被引：0

作者：

de Lima, Henrique F. ^{[1
]}

Leite, Ary V. F. ^{[1
]}

Velasquez, Marco Antonio L. ^{[1
]}

机构：

[1] Univ Fed Campina Grande, Dept Matemat, BR-58429970 Campina Grande, PB, Brazil

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2025年 / 28卷 / 01期

关键词：

Einstein manifolds; CMC hypersurfaces; Totally umbilical hypersurfaces; Strongly stable hypersurfaces; First stability eigenvalue; CONSTANT MEAN-CURVATURE; RIGIDITY THEOREMS; SCALAR CURVATURE; SURFACES;

D O I：

10.1007/s11040-025-09499-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the umbilicity of constant mean curvature (CMC) complete hypersurfaces immersed in an Einstein manifold satisfying appropriate curvature constraints. In this setting, we obtain new characterization results for totally umbilical hypersurfaces via suitable maximum principles which deal with the notions of convergence to zero at infinity and polynomial volume growth. Afterwards, we establish optimal estimates for the first eigenvalue of the stability operator of CMC compact hypersurfaces in such an Einstein manifold. In particular, we derive a nonexistence result concerning strongly stable CMC hypersurfaces.

引用

页数：22