3 papers
math.DG2025
Isoperimetric inequalities involving Steklov eigenvalues on surfaces
Romain Petrides
We give results on optimal constants of isoperimetric inequalities involving Steklov eigenvalues on surfaces with boundary. We both consider this question on Riemannian surfaces wi…
math.DG2025
Existence of metrics maximizing the first Laplace eigenvalue on closed surfaces
Mikhail Karpukhin, Romain Petrides, Daniel Stern
Building on seminal work of Nadirashvili and previous work of the authors, we prove the existence of metrics maximizing the area-normalized first eigenvalue of the Laplacian on eve…
math.DG2023
Laplace eigenvalues and non-planar minimal spheres into 3-dimensional ellipsoids
Romain Petrides
We give a sufficient condition for branched minimal immersions of spheres into ellipsoids to be embedded: we show that if the coordinate functions of the branched minimal immersion…