4 papers
Geometric bounds for low Steklov eigenvalues of finite volume hyperbolic surfaces
Asma Hassannezhad, Antoine Métras, Hélène Perrin
We obtain geometric lower bounds for the low Steklov eigenvalues of finite-volume hyperbolic surfaces with geodesic boundary. The bounds we obtain depend on the length of a shortes…
Critical lengths of Steklov eigenvalues of hypersurfaces of revolution in Euclidean space
Antoine Métras, Léonard Tschanz
We study the Steklov problem on hypersurfaces of revolution with two boundary components in Euclidean space. In a recent article, the phenomenon of critical length, at which a Stek…
Tubes and Steklov eigenvalues in negatively curved manifolds
Ara Basmajian, Jade Brisson, Asma Hassannezhad +1
We consider the Steklov eigenvalue problem on a compact pinched negatively curved manifold of dimension at least three with totally geodesic boundaries. We obtain a geometric l…
Dirac Eigenvalue Optimisation and Harmonic Maps to Complex Projective Spaces
Mikhail Karpukhin, Antoine Métras, Iosif Polterovich
Consider a Dirac operator on an oriented compact surface endowed with a Riemannian metric and spin structure. Provided the area and the conformal class are fixed, how small can the…