Sharp Minkowski-Type Inequality in Cartan-Hadamard 3-Spaces
Abstract
In this paper, we prove a sharp Minkowski-type inequality in Cartan-Hadamard 3-spaces using harmonic mean curvature flow and improve the known estimates for total mean curvature in hyperbolic 3-space. In particular, we sharpen Ghomi-Spruck's result in ghomi-spruck2023 by retaining the volume contribution in the monotonicity argument. As a corollary, we obtain a comparison theorem relating the total mean curvature of convex surfaces in Cartan-Hadamard 3-spaces to their enclosed volume.
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