Weinstock inequalities for outward-minimizing domains

Chaoqun Gao; Yong Wei; Rong Zhou

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arXiv · 2608.11841

Weinstock inequalities for outward-minimizing domains

Chaoqun Gao·Yong Wei·Rong Zhou

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Abstract

We prove sharp Weinstock inequalities for the first nonzero Steklov eigenvalue of smooth outward-minimizing domains in Euclidean space and hyperbolic space. The method is based on the weak inverse mean curvature flow of Huisken--Ilmanen. The main new ingredient is an endpoint distributional monotonicity argument obtained from the calibrated weak formulation and the Gauss--Green formula for divergence-measure fields.

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Chaoqun Gao, Yong Wei, Rong Zhou. 2026-08-12. Weinstock inequalities for outward-minimizing domains. https://arxiv.org/abs/2608.11841

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