4 citations · 5 across the 9 of their papers we have counts for
8 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.…
Laplace and Steklov extremal metrics via -harmonic maps
Mikhail Karpukhin, Antoine Métras
We present a unified description of extremal metrics for the Laplace and Steklov eigenvalues on manifolds of arbitrary dimension using the notion of -harmonic maps. Our approach…
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…
Maximal metrics for the first Steklov eigenvalue on surfaces
Mikhail Karpukhin
In recent years, eigenvalue optimization problems have received a lot of attention, in particular, due to their connection with the theory of minimal surfaces. In the present paper…
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…
Bounds between Laplace and Steklov eigenvalues on nonnegatively curved manifolds
Mikhail A. Karpukhin
Consider a compact Riemannian manifold with boundary. In this short note we prove that under certain positive curvature assumptions on the manifold and its boundary the Steklov eig…
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…