Estimates on the Neumann and Steklov principal eigenvalues of collapsing domains
Paolo Acampora, Vincenzo Amato, Emanuele Cristoforoni · Communications in Contemporary Mathematics · 2025
We investigate the relationship between the Neumann and Steklov principal eigenvalues emerging from the study of collapsing convex domains in [Formula: see text]. Such a relationship allows us to give a partial proof of a conjecture concerning estimates of the ratio of the former to the latter: we show that thinning triangles maximize the ratio among convex thinning sets, while thinning rectangles minimize the ratio among convex thinning with some symmetry property.