José Espinar: An overdetermined eigenvalue problem and the Critical Catenoid conjecture.

(29 avril 2024/April 29, 2024) Seminar Spectral Geometry in the clouds

José Espinar (University of Granada): An overdetermined eigenvalue problem and the Critical Catenoid conjecture.

Abstract: We consider the eigenvalue problem ∆S 2 ξ + 2ξ = 0 in Ω and ξ = 0 along ∂Ω, being Ω the complement of a disjoint and finite union of smooth and bounded simply connected regions in the two-sphere S 2 . Imposing that k∇ξk is locally constant along ∂Ω and that ξ has infinitely many maximum points, we are able to classify positive solutions as the rotationally symmetric ones. As a consequence, we obtain a characterization of the critical catenoid as the only embedded free boundary minimal annulus in the unit ball whose support function has infinitely many critical points.