16 citations · 49 across the 16 of their papers we have counts for
18 papers
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…
Free boundary minimal surfaces and overdetermined boundary value problems
Nikolai Nadirashvili, Alexei V. Penskoi
In this paper we establish a connection between free boundary minimal surfaces in a ball in and free boundary cones arising in a one-phase problem. We prove that a d…
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 on Multiplicities of Laplace-Beltrami Operator Eigenvalues on the Real Projective Plane
Aleksandr S. Berdnikov, Nikolai S. Nadirashvili, Alexei V. Penskoi
The known upper bounds for the multiplicities of the Laplace-Beltrami operator eigenvalues on the real projective plane are improved for the eigenvalues with even indexes. Upper bo…
An isoperimetric inequality for the second non-zero eigenvalue of the Laplacian on the projective plane
Nikolai S. Nadirashvili, Alexei V. Penskoi
We prove an isoperimetric inequality for the second non-zero eigenvalue of the Laplace-Beltrami operator on the real projective plane. For a metric of the unit area this eigenvalue…
Generalized Lawson tori and Klein bottles
Alexei V. Penskoi
Using Takahashi theorem we propose an approach to extend known families of minimal tori in spheres. As an example, the well-known two-parametric family of Lawson tau-surfaces inclu…