A spectral volume comparison for manifolds with weakly convex boundary
Year: 2026
Type: article
Abstract: We establish the Bonnet–Myers theorem and the Bishop–Gromov volume comparison theorem in the spectral sense for manifolds with weakly convex boundary. For , let be a connected compact smooth ‐manifold with weakly convex boundary . If there exists a positive function that satisfies: where denotes the smallest eigenvalue of the Ricci tensor, is the unit co‐normal vector field of in , then the diameter of satisfies . If, in addition, attains its minimum on the boundary , we obtain a sharp upper bound for the volume of : , with equality holding if and only if is isometric to the unit round hemisphere .
DOI: 10.1112/blms.70473
Author: Jia Li
Institution: Xiamen University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408344941