Prescription of the Robin spectrum

Xiang He; Zuoqin Wang

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arXiv · 2503.01451

Prescription of the Robin spectrum

Xiang He·Zuoqin Wang

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Abstract

Let $M$ be a compact connected smooth manifold with smooth boundary, and let $\rho$ be a positive continuous function on the boundary which is served as the Robin parameter. In this paper, we study three problems concerning the prescription of finite Robin spectrum: (1) Prescribing finitely many Robin eigenvalues and the volume. (2) Within a fixed conformal class, prescribing the multiplicities of finitely many Robin eigenvalues. (3) Within a fixed conformal class, prescribing finitely many distinct Robin eigenvalues and the volume. A key step in our method is to solve the corresponding problems for the Dirichlet spectrum. As a consequence, we also obtain analogous results for the Dirichlet case.

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Xiang He, Zuoqin Wang. 2025-03-03. Prescription of the Robin spectrum. https://arxiv.org/abs/2503.01451

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