4 citations · 4 across the 3 of their papers we have counts for
8 papers
Weyl's law for the Steklov problem on surfaces with rough boundary
Mikhail Karpukhin, Jean Lagacé, Iosif Polterovich
The validity of Weyl's law for the Steklov problem on domains with Lipschitz boundaries is a well-known open question in spectral geometry. We answer this question in two dimension…
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…
The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander's rediscovered manuscript
Alexandre Girouard, Mikhail Karpukhin, Michael Levitin +1
How close is the Dirichlet-to-Neumann (DtN) map to the square root of the corresponding boundary Laplacian? This question has been actively investigated in recent years. Somewhat s…
Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems
Alexandre Girouard, Mikhail Karpukhin, Jean Lagacé
We associate a sequence of variational eigenvalues to any Radon measure on a compact Riemannian manifold. For particular choices of measures, we recover the Laplace, Steklov and ot…
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…