Floquet-Bloch functions on non-simply connected manifolds, the Aharonov-Bohm fluxes, and conformal invariants of immersed surfaces

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Several complex variables and analytic spaces (32-XX)

Cites Work

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Spectral curves for Cauchy-Riemann operators on punctured elliptic curves
The Moutard transformation of two-dimensional Dirac operators and the conformal geometry of surfaces in four-dimensional space
Bethe-Sommerfeld conjecture
The spectrum band structure of the three-dimensional Schrödinger operator with periodic potential
Asymptotic formulas for the eigenvalues of a periodic Schrödinger operator and the Bethe-Sommerfeld conjecture
The periodic problem for the Korteweg-de Vries equation
Green's function asymptotics of periodic elliptic operators on abelian coverings of compact manifolds
The Weierstrass representation of closed surfaces in \(\mathbb{R}^3\)
The Moutard transformation of two-dimensional Dirac operators and Möbius geometry
Surfaces in the four-space and the Davey-Stewartson equations
Significance of Electromagnetic Potentials in the Quantum Theory
Perturbation theory for the periodic multidimensional Schrodinger operator and the Bethe-Sommerfeld conjecture
Euclidean Minimal Tori with Planar Ends and Elliptic Solitons
Spectral theory of two-dimensional periodic operators and its applications
Periodic Schrödinger Operators on a Manifold
NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
Modified Novikov--Veselov equation and differential geometry of surfaces
Induced Surfaces and Their Integrable Dynamics
Two-dimensional Dirac operator and the theory of surfaces
Surfaces via spinors and soliton equations
Geometry and quasiclassical quantization of magnetic monopoles

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