3 citations · 6 across the 9 of their papers we have counts for
12 papers
Index and nullity of minimal surfaces via representation theory
Mikhail Karpukhin, Mario B. Schulz
We develop a representation-theoretic approach to determine the Morse index and nullity of an embedded minimal surface based only on its topology and symmetry group. The method com…
Nonorientable Minimal Surfaces Embedded in the Round -sphere
Mikhail Karpukhin, Robert Kusner, Peter McGrath +1
We show that every closed, nonorientable surface can be minimally embedded in , providing in particular the first known examples of embedded, nonorientable minimal su…
Existence of metrics maximizing the first Laplace eigenvalue on closed surfaces
Mikhail Karpukhin, Romain Petrides, Daniel Stern
Building on seminal work of Nadirashvili and previous work of the authors, we prove the existence of metrics maximizing the area-normalized first eigenvalue of the Laplacian on eve…
Large topology asymptotics for spectrally extremal minimal surfaces in and
Mikhail Karpukhin, Peter McGrath, Daniel Stern
In recent work with Kusner, we developed a method, based on the equivariant optimization of Laplace and Steklov eigenvalues, for producing minimal surfaces of prescribed topology i…
Embedded minimal surfaces in and via equivariant eigenvalue optimization
Mikhail Karpukhin, Robert Kusner, Peter McGrath +1
In 1970, Lawson solved the topological realization problem for minimal surfaces in the sphere, showing that any closed orientable surface can be minimally embedded in $\mathbb{S}^3…
Existence of harmonic maps and eigenvalue optimization in higher dimensions
Mikhail Karpukhin, Daniel Stern
We prove the existence of nonconstant harmonic maps of optimal regularity from an arbitrary closed manifold of dimension to any closed, non-aspherical manifold …
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…
Min-max harmonic maps and a new characterization of conformal eigenvalues
Mikhail Karpukhin, Daniel L. Stern
Given a surface and a fixed conformal class one defines to be the supremum of the -th nontrivial Laplacian eigenvalue over all metrics of unit volume…
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…