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Eigenvalue optimization via a first-variation formula
Denis Vinokurov
We compute the Clarke subdifferential of the th eigenvalue functional on the space of self-adjoint operators, obtaining a first-variation formula that remains valid even when th…
Geometric bounds for Steklov and weighted Neumann eigenvalues on Euclidean domains
Denis Vinokurov
We obtain sharp upper bounds for the first two nonzero Steklov eigenvalues among bounded domains in Euclidean spaces of dimension under a natural normalization involving…
Eigenvalue optimization in higher dimensions and -harmonic maps
Denis Vinokurov
We prove existence results for optimization problems for the th Laplace eigenvalue on closed Riemannian manifolds of dimension , depending on the choice of normalizati…
Maximizing higher eigenvalues in dimensions three and above
Denis Vinokurov
We study the problem of maximizing the -th eigenvalue functional over the class of absolutely continuous measures on a closed Riemannian manifold of dimension . Extendi…
Conformal optimization of eigenvalues on surfaces with symmetries
Denis Vinokurov
Given a conformal action of a discrete group on a Riemann surface, we study the maximization of Laplace and Steklov eigenvalues within a conformal class, considering metrics invari…