Statistical properties of the spectra of Laplace-Beltrami operators on Liouville surfaces
From MaRDI portal
Publication:4323897
DOI10.1070/RM1993v048n04ABEH001052zbMath0838.58041OpenAlexW1973641167MaRDI QIDQ4323897
Denis V. Kosygin, A. A. Minasov, Yakov G. Sinai
Publication date: 9 March 1995
Published in: Russian Mathematical Surveys (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1070/rm1993v048n04abeh001052
Asymptotic results on counting functions for algebraic and topological structures (11N45) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)
Related Items
Semiclassical quantization rules near separatrices, Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae, Spectrum of the Laplace operator on closed surfaces, Spectral series of the Schrödinger operator in thin waveguides with periodic structure. I: Adiabatic approximation and semiclassical asymptotics in the 2D case, Explicit formula for the spectral counting function of the Laplace operator on a compact Riemannian surface of genus \(g>1\), Spectral series of the Schrödinger operator in a thin waveguide with a periodic structure. II: Closed three-dimensional waveguide in a magnetic field, Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber, Singular semi-classical approximation on Liouville surfaces, Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta, and proof of the projective Obata conjecture for two-dimensional pseudo-Riemannian metrics, The asymptotic eigenfunctions of the operator \(\nabla D(x,y)\nabla\) corresponding to Liouville metrics and waves on water captured by bottom irregularities, Riemannian manifolds with uniformly bounded eigenfunctions, Riemannian manifolds with maximal eigenfunction growth