112 citations · 272 across the 14 of their papers we have counts for
14 papers
The Geometry of Morphogenesis and the Morphogenetic Field Concept
Nadya Morozova, Mikhail Shubin
The process of morphogenesis, which can be defined as an evolution of the form of an organism, is one of the most intriguing mysteries in the life sciences. It is clear, that gene…
Semiclassical Asymptotics on Manifolds with Boundary
Nilufer Koldan, Igor Prokhorenkov, Mikhail Shubin
We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we…
Gauge optimization and spectral properties of magnetic Schrödinger operators
Vladimir Kondratiev, Vladimir Maz'ya, Mikhail Shubin
We establish new necessary and sufficient conditions for the discreteness of spectrum and strict positivity of magnetic Schrödinger operators with a positive scalar potential. They…
Geometric Theory of Lattice Vibrations and Specific Heat
Mikhail Shubin, Toshikazu Sunada
We discuss, from a geometric standpoint, the specific heat of a solid. This is a classical subject in solid state physics which dates back to a pioneering work by Einstein (1907) a…
The Miura Map on the Line
Thomas Kappeler, Peter Perry, Mikhail Shubin +1
The Miura map (introduced by Miura) is a nonlinear map between function spaces which transforms smooth solutions of the modified Korteweg - de Vries equation (mKdV) to solutions of…
Can one see the fundamental frequency of a drum?
Vladimir Maz'ya, Mikhail Shubin
We establish two-sided estimates for the fundamental frequency (the lowest eigenvalue) of the Laplacian in an open subset G of R^n with the Dirichlet boundary condition. This is do…