Spectral geometry: direct and inverse problems. With an appendix by G. Besson
From MaRDI portal
Publication:1085849
DOI10.1007/BFb0076330zbMath0608.58001MaRDI QIDQ1085849
Publication date: 1986
Published in: Lecture Notes in Mathematics (Search for Journal in Brave)
heat equationLaplace-Beltrami operatorspectral geometrysymmetrization processisoperimetric methodsvariational characterizations of the eigenvalues
Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20) Research exposition (monographs, survey articles) pertaining to global analysis (58-02) Heat and other parabolic equation methods for PDEs on manifolds (58J35)
Related Items (53)
Geometric structures and the Laplace spectrum, Part II ⋮ Embedding Riemannian manifolds by the heat kernel of the connection Laplacian ⋮ A Borg-Levinson theorem for magnetic Schrödinger operators on a Riemannian manifold ⋮ Isoperimetric bounds for lower-order eigenvalues ⋮ Lifschitz Tail and Wiener Sausage on hyperbolic space ⋮ General formula for lower bound of the first eigenvalue on Riemannian manifolds ⋮ Quelques théorèmes d'annulation et de majoration d'invariants géométriques ⋮ Some eigenvalue comparison theorems of Finsler p-Laplacian ⋮ Coupling, spectral gap and related topics. II ⋮ Principe de Dirichlet pour les formes différentielles ⋮ Elliptic equations on manifolds and isoperimetric inequalities ⋮ Approximation of the spectral action functional in the case of \(\tau\)-compact resolvents ⋮ Feynman-Kac formula for perturbations of order \(\leq 1\), and noncommutative geometry ⋮ On the first eigenvalue of the Neumann problem ⋮ Accelerating diffusion on compact Riemannian surfaces by incompressible drift ⋮ Graph connection Laplacian and random matrices with random blocks ⋮ Isospectral Alexandrov spaces ⋮ The spectrum of the Laplacian: A geometric approach ⋮ A Gaussian estimate for the heat kernel on differential forms and application to the Riesz transform ⋮ Conformal upper bounds for the eigenvalues of the Laplacian and Steklov problem ⋮ Lower curvature bounds, Toponogov's theorem, and bounded topology. II ⋮ Eigenvalues, inequalities and ergodic theory ⋮ The linear request problem ⋮ Periodic magnetic geodesics on Heisenberg manifolds ⋮ Spectrum of the Laplacian with weights ⋮ Gaussian heat kernel estimates: from functions to forms ⋮ Think globally, fit locally under the manifold setup: asymptotic analysis of locally linear embedding ⋮ Asymptotic expansion of the Faber-Krahn profile of a compact Riemannian manifold ⋮ The spectral length of a map between Riemannian manifolds ⋮ The geometry of Markov diffusion generators ⋮ Accelerating diffusion by incompressible drift on the two-dimensional torus ⋮ Extremal properties of eigenvalues for a metric graph. ⋮ Unnamed Item ⋮ Transonic shocks in multidimensional divergent nozzles ⋮ Pointwise symmetrization inequalities for Sobolev functions and applications ⋮ Implications of energy conditions on standard static space-times ⋮ Embeddings of Riemannian manifolds with finite eigenvector fields of connection Laplacian ⋮ Affine symplectic geometry. I: Applications to geometric inequalities ⋮ The embedding dimension of Laplacian eigenfunction maps ⋮ On how to use drift to push the spectral gap of a diffusion on $S^{2}$ to infinity ⋮ Semicontinuity of eigenvalues under intrinsic flat convergence ⋮ Spectral analysis of second-order elliptic operators on noncompact manifolds ⋮ D'un résultat hilbertien à un principe de comparaison entre spectres. Applications ⋮ Lifschitz tail on hyperbolic space: Neumann conditions ⋮ Local well-posedness for the quadratic Schrödinger equation in two-dimensional compact manifolds with boundary ⋮ Number of bound states and estimates on some geometric invariants ⋮ D'un résultat hilbertien à un principe de comparaison entre spectres. Applications ⋮ Wave-shape oscillatory model for nonstationary periodic time series analysis ⋮ Eigenvalue estimates for the weighted Laplacian on a Riemannian manifold ⋮ Mathematical analysis and solution methodology for an inverse spectral problem arising in the design of optical waveguides ⋮ The length spectrum of Riemannian two-step nilmanifolds1 ⋮ The Faber-Krahn type isoperimetric inequalities for a graph ⋮ Betti numbers on a tower of coverings
This page was built for publication: Spectral geometry: direct and inverse problems. With an appendix by G. Besson
