Samuel Pérez-Ayala

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

We study the variational properties of the spectrum of the Dirichlet-to-Robin map $\mathcal{D}_g$ on connected compact manifolds with boundary of dimension at least three. For the first eigenvalue, we show that Type II Yamabe metrics extremize the first normalized eigenvalue functional, and we characterize all extremal...