2023/10/10 by Espinar, José M., Marín, Diego A. · 3 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2310.06705
We consider the eigenvalue problem Δ^\mathbbS2 ξ+ 2 ξ=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 \mathbbS2. Imposing that |∇ ξ| 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.