https://neckpinch.com/authors/ovidiu-munteanu/New arXiv papers by Ovidiu Munteanu, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2309.13749arxiv:2309.13749Sun, 24 Sep 2023 00:00:00 GMTOvidiu Munteanu, Jiaping Wang — The classical Minkowski inequality implies that the volume of a bounded convex domain is controlled from above by the integral of the mean curvature of its boundary. In this note, we establish an analogous inequality without the convexity assumption for all bounded smooth domains in a complete manifold with its bottom spectrum being suitably large relative to its Ricci curvature lower bound. An immediate implication is the nonexistence of embedded compact minimal hypersurfaces in such manifolds. This nonexistence issue is also considered for steady and expanding Ricci solitons.Ricci solitonsBoundaries & non-compactGeometric inequalitiesEigenvalues & spectrumMinimal & CMC surfaces