9 citations · 11 across the 7 of their papers we have counts for
7 papers
Existence and Regularity of Extremal Metrics for the Conformal Dirichlet-to-Robin Map
Samuel Pérez-Ayala
We study the variational properties of the spectrum of the Dirichlet-to-Robin map on connected compact manifolds with boundary of dimension at least three. For the…
Sharp Spectral Bounds for the -Laplacian and Polyharmonic Operators on Asymptotically Hyperbolic Manifolds
Samuel Pérez-Ayala
We derive sharp bounds for three types of eigenvalue problems. First, we derive an upper bound for the first -Dirichlet eigenvalue on conformally compact (CC) spaces. As a conse…
Holography and Cheeger constant of asymptotically CMC submanifolds
Samuel Pérez-Ayala, Aaron J. Tyrrell
Let be an asymptotically hyperbolic manifold. We compute the Cheeger constant of conformally compact asymptotically constant mean curvature submanifolds $ ι: Y^{k+1…
First Eigenvalue Estimates for Asymptotically Hyperbolic Manifolds and their Submanifolds
Samuel Pérez-Ayala, Aaron J. Tyrrell
We derive a sharp upper bound for the first eigenvalue of the -Laplacian on asymptotically hyperbolic manifolds for . We then prove that a particular class…
Extremal metrics for the Paneitz Operator on closed four-Manifolds
Samuel Pérez-Ayala
Let be a closed Riemannian manifold of dimension four. We investigate the properties of metrics which are critical points of the eigenvalues of the Paneitz operator when…
Extremal Eigenvalues Of The Conformal Laplacian Under Sire-Xu Normalization
Samuel Pérez-Ayala
Let be a closed Riemannian manifold of dimension . We study the variational properties of the -th eigenvalue functional $\tilde g\in[g] \mapsto λ_k(L_{\tilde g…
Variational Properties Of The Second Eigenvalue Of The Conformal Laplacian
Matthew J. Gursky, Samuel Pérez-Ayala
Let be a closed Riemannian manifold of dimension . Assume is a conformal class for which the Conformal Laplacian has at least two negative eigenvalues…