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.DG2024
Non planar free boundary minimal disks into ellipsoids
Romain Petrides
We prove the existence of embedded non planar free boundary minimal disks into rotationally symmetric ellipsoids of . The construction relies on the optimization of c…
math.AP2024
A variational method for functionals depending on eigenvalues
Romain Petrides
We perform a systematic variational method for functionals depending on eigenvalues of Riemannian manifolds. It is based on a new concept of Palais Smale sequences that can be cons…