학술
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Sharp Minkowski-Type Inequality in Cartan-Hadamard 3-Spaces
arXiv Math
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이 매체는 공공·자유 라이선스로 본문을 직접 표시합니다.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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