Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Petrides, Romain"'
Autor:
Petrides, Romain
We prove the existence of optimal metrics for a wide class of combinations of Laplace eigenvalues on closed orientable surfaces of any genus. The optimal metrics are explicitely related to Laplace minimal eigenmaps, defined as branched minimal immers
Externí odkaz:
http://arxiv.org/abs/2410.13347
Autor:
Petrides, Romain, Tewodrose, David
We set up a new framework to study critical points of functionals defined as combinations of eigenvalues of operators with respect to a given set of parameters: Riemannian metrics, potentials, etc. Our setting builds upon Clarke's differentiation the
Externí odkaz:
http://arxiv.org/abs/2403.07841
Autor:
Petrides, Romain
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 are first or second eigenfunctions with respect to a natural metric o
Externí odkaz:
http://arxiv.org/abs/2304.12119
Autor:
Petrides, Romain
We prove the existence of embedded non planar free boundary minimal disks into rotationally symmetric ellipsoids of $\mathbb{R}^3$. The construction relies on the optimization of combinations of first and second Steklov eigenvalues renormalized by th
Externí odkaz:
http://arxiv.org/abs/2304.12111
Autor:
Petrides, Romain
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 Riemannian manifold of dimension $n\geq 3$.
Externí odkaz:
http://arxiv.org/abs/2211.15636
Autor:
Petrides, Romain
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 constructed thanks to a generalization of classical min-max methods on $C^
Externí odkaz:
http://arxiv.org/abs/2211.15632
Autor:
Laurain, PAul, Petrides, Romain
We perform the classical Ginzburg-Landau analysis originated from the celebrated paper by Bethuel, Brezis, H\'elein for optimal boundary data. More precisely, we give optimal regularity assumptions on the boundary curve of planar domains and Dirichle
Externí odkaz:
http://arxiv.org/abs/2111.14717
Autor:
Matthiesen, Henrik, Petrides, Romain
We show rigidity of the first conformal Steklov eigenvalue on annuli and M\"obius bands. The proof relies, among others, on uniqueness results due to Fraser--Schoen, a compactness theorem of the second named author, and recent work of the authors on
Externí odkaz:
http://arxiv.org/abs/2006.04364
Autor:
Matthiesen, Henrik, Petrides, Romain
For any compact surface $\Sigma$ with smooth, non-empty boundary, we construct a free boundary minimal immersion into a Euclidean Ball $\mathbb{B}^N$ where $N$ is controlled in terms of the topology of $\Sigma$. We obtain these as maximizing metrics
Externí odkaz:
http://arxiv.org/abs/2004.06051
