29 citations · 192 across the 45 of their papers we have counts for
11 papers · 1 filter
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…
Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces
Mikhail Karpukhin, Mickaël Nahon, Iosif Polterovich +1
We prove stability estimates for the isoperimetric inequalities for the first and the second nonzero Laplace eigenvalues on surfaces, both globally and in a fixed conformal class.…
Conformally maximal metrics for Laplace eigenvalues on surfaces
Mikhail Karpukhin, Nikolai Nadirashvili, Alexei V. Penskoi +1
The paper is concerned with the maximization of Laplace eigenvalues on surfaces of given volume with a Riemannian metric in a fixed conformal class. A significant progress on this…
An isoperimetric inequality for Laplace eigenvalues on the sphere
Mikhail Karpukhin, Nikolai Nadirashvili, Alexei V. Penskoi +1
We show that for any positive integer k, the k-th nonzero eigenvalue of the Laplace-Beltrami operator on the two-dimensional sphere endowed with a Riemannian metric of unit area, i…
Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound
Asma Hassannezhad, Gerasim Kokarev, Iosif Polterovich
We revisit classical eigenvalue inequalities due to Buser, Cheng, and Gromov on closed Riemannian manifolds, and prove the versions of these results for the Dirichlet and Neumann b…
Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces
Mikhail Karpukhin, Gerasim Kokarev, Iosif Polterovich
We prove two explicit bounds for the multiplicities of Steklov eigenvalues on compact surfaces with boundary. One of the bounds depends only on the genus of a surface and the…