Investigates V-static-type equations, yielding integral inequalities and rigidity results in manifolds with boundaries.
In this paper, we investigate compact Riemannian manifolds with boundary satisfying V-static-type equation. By combining a generalized Reilly formula with Steklov-type boundary value problems, we derive new integral inequalities for geometric quantities associated with the boundary. These inequalities lead to rigidity results, including characterizations of geodesic balls in space forms. In particular, these results provide new insights into classical rigidity theorems.
No takes yet. Share an insight, caveat, or question.
Maria Andrade (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: