https://neckpinch.com/authors/mohammad-ghomi/New arXiv papers by Mohammad Ghomi, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2206.06554/arxiv:2206.06554Tue, 14 Jun 2022 00:00:00 GMTMohammad Ghomi, Joel Spruck — Using harmonic mean curvature flow, we establish a sharp Minkowski type lower bound for total mean curvature of convex surfaces with a given area in Cartan-Hadamard 3-manifolds. This inequality also improves the known estimates for total mean curvature in hyperbolic 3-space. As an application, we obtain a Bonnesen-style isoperimetric inequality for surfaces with convex distance function in nonpositively curved 3-spaces, via monotonicity results for total mean curvature. This connection between the Minkowski and isoperimetric inequalities is extended to Cartan-Hadamard manifolds of any dimension.Mean curvature flow3-manifoldsGeometric inequalities