3 citations · 6 across the 3 of their papers we have counts for
5 papers
From Steklov to Laplace: free boundary minimal surfaces with many boundary components
Mikhail Karpukhin, Daniel Stern
In the present paper, we study sharp isoperimetric inequalities for the first Steklov eigenvalue on surfaces with fixed genus and large number of boundary components. We…
Spherical conical metrics and harmonic maps to spheres
Mikhail Karpukhin, Xuwen Zhu
A spherical conical metric on a surface is a metric of constant curvature with finitely many isolated conical singularities. The uniformization problem for such metrics…
Index of minimal spheres and isoperimetric eigenvalue inequalities
Mikhail Karpukhin
In the present paper we use twistor theory in order to solve two problems related to harmonic maps from surfaces to Euclidean spheres . First, we propose a new approa…
On the Friedlander-Nadirashvili invariants of surfaces
Mikhail Karpukhin, Vladimir Medvedev
Let be a closed smooth manifold. In 1999, L. Friedlander and N. Nadirashvili introduced a new differential invariant using the first normalized nonzero eigenvalue of t…
Spectral properties of a family of minimal tori of revolution in five-dimensional sphere
Mikhail Karpukhin
The normalized eigenvalues of the Laplace-Beltrami operator can be considered as functionals on the space of all Riemannian metrics on a fixed surface . In recent…