works on
conformal geometry 1eigenvalue optimization 1manifolds with boundary 1spectral theory 1yamabe problem 1

From the 1 of 4 linked papers with an AI index.

activity
20242026
collaborators

4 papers

math.DG2026

Existence and Regularity of Extremal Metrics for the Conformal Dirichlet-to-Robin Map

Samuel Pérez-Ayala

The paper studies how the spectrum of the Dirichlet-to-Robin map on compact manifolds with boundary behaves under conformal changes, showing that Type II Yamabe metrics extremize t…

math.DG2026

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…

math.DG2025

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+…

math.DG2024

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 clas…