17 citations · 20 across the 3 of their papers we have counts for
5 papers
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 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…
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…