Work

Weinstock inequalities for outward-minimizing domains

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.11841

Authors: Gao, Chaoqun, Wei, Yong, Zhou, Rong

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation, National Key Research and Development Program of China, Fundamental Research Funds for the Central Universities

Awards: G130972461, G1470452843, G2150776504

OpenAlex ID: W7202339365

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