Diego A. Mar'in

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math.AP2024

Extremal domains in $S^{2}$ : Geometric and Analytic methods

José M. Espinar, Diego A. Marín

In this article, we study domains $Ω \subset S^{2}$ that support positive solutions of the overdetermined problem $Δ u + f (u, ∣\nabla u ∣) = 0 in Ω,$ subject to…

math.AP2023

An overdetermined eigenvalue problem and the Critical Catenoid conjecture

José M. Espinar, Diego A. Marín

We consider the eigenvalue problem $Δ^{S^{2}} ξ + 2 ξ = 0$ in $Ω$ and $ξ = 0$ along $\partial Ω$ , being $Ω$ the complement of a disjoint and finite union of smooth and bound…

Extremal domains in S2: Geometric and Analytic methods

An overdetermined eigenvalue problem and the Critical Catenoid conjecture

Extremal domains in $S^{2}$ : Geometric and Analytic methods