17 citations · 26 across the 11 of their papers we have counts for
14 papers
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…
Maximizing one Laplace eigenvalue on n-dimensional manifolds
Romain Petrides
We prove existence and regularity results for the problem of maximization of one Laplace eigenvalue with respect to metrics of same volume lying in a conformal class of a Riemannia…
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…
Existence of Ginzburg-Landau minimizers with optimal boundary data and applications
PAul Laurain, Romain Petrides
We perform the classical Ginzburg-Landau analysis originated from the celebrated paper by Bethuel, Brezis, Hélein for optimal boundary data. More precisely, we give optimal regular…
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…
Regularity and quantification for harmonic maps with free boundary
Paul Laurain, Romain Petrides
We prove a quantification result for harmonic maps with free boundary from arbitrary Riemannian surfaces into the unit ball of with bounded energy. This general…
Existence and regularity of maximal metrics for the first Laplace eigenvalue on surfaces
Romain Petrides
We investigate in this paper the existence of a metric which maximizes the first eigenvalue of the Laplacian on Riemannian surfaces. We first prove that, in a given conformal class…
On a rigidity result for the first conformal eigenvalue of the Laplacian
Romain Petrides
Given a smooth compact Riemannian manifold without boundary of dimension , we consider the first conformal eigenvalue which is by definition the supremum of the fi…
Maximization of the second conformal eigenvalue of spheres
Romain Petrides
We establish in this paper an upper bound on the second eigenvalue of n-dimensional spheres in the conformal class of the round sphere. This upper bound holds in all dimensions and…