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arXiv · 2603.19646

Sharp Minkowski-Type Inequality in Cartan-Hadamard 3-Spaces

Fang Hong
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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 \cite{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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Fang Hong. 2026-03-20. Sharp Minkowski-Type Inequality in Cartan-Hadamard 3-Spaces. https://arxiv.org/abs/2603.19646

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