17 citations · 26 across the 11 of their papers we have counts for
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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…
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…
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…
A remark on the rigidity of the first conformal Steklov eigenvalue
Henrik Matthiesen, Romain Petrides
We show rigidity of the first conformal Steklov eigenvalue on annuli and Möbius bands. The proof relies, among others, on uniqueness results due to Fraser--Schoen, a compactness th…
Free boundary minimal surfaces of any topological type in Euclidean balls via shape optimization
Henrik Matthiesen, Romain Petrides
For any compact surface with smooth, non-empty boundary, we construct a free boundary minimal immersion into a Euclidean Ball where is controlled in terms of…
Existence of Min-Max Free Boundary Disks Releasing the Width of a Manifold
Paul Laurain, Romain Petrides
We perform a replacement procedure in order to produce a free boundary minimal surface whose area achieves the min-max value over all disk sweepouts of a manifold whose boundary li…
Monotonicity results for the first Steklov eigenvalue on compact surfaces
Henrik Matthiesen, Romain Petrides
We show several results comparing sharp eigenvalue bounds for the first Steklov eigenvalue on surfaces under change of the topology. Among others, we obtain strict monotonicity in…