Samuel Pérez-Ayala

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math.DG2026

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 $D_{g}$ on connected compact manifolds with boundary of dimension at least three. For the…

math.DG2026

Sharp Spectral Bounds for the $p$ -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 $p$ -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 $(M^{n + 1}, g_{+})$ be an asymptotically hyperbolic manifold. We compute the Cheeger constant of conformally compact asymptotically constant mean curvature submanifolds $ ι: Y^{k+1…

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 $λ_{1, p}$ of the $p$ -Laplacian on asymptotically hyperbolic manifolds for $1 < p < \infty$ . We then prove that a particular class…

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

Sharp Spectral Bounds for the p-Laplacian and Polyharmonic Operators on Asymptotically Hyperbolic Manifolds

Holography and Cheeger constant of asymptotically CMC submanifolds

First Eigenvalue Estimates for Asymptotically Hyperbolic Manifolds and their Submanifolds

Sharp Spectral Bounds for the $p$ -Laplacian and Polyharmonic Operators on Asymptotically Hyperbolic Manifolds