Work

Rigidity for inscribed radius estimate of asymptotically hyperbolic Einstein manifold

Year: 2024

Type: article

Abstract: The inscribed radius of a compact manifold with boundary is bounded above if its Ricci curvature and mean curvature are bounded from below. The rigidity result implies that the upper bound can be achieved only in space form. In this paper, we generalize this result to asymptotically hyperbolic (AH) Einstein manifold. We get an upper bound of the relative volume of AH manifold and if we combine it with the recent work of Wang and Zhou, then the rigidity is obtained.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/proc/16955

Author: Xiaoshang Jin

Institution: Huazhong University of Science and Technology

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G745707110