Some topics in spectral geometry
Special invariant operators I
The aim of the first part of a series of papers is to give a description of invariant differential operators on manifolds with an almost Hermitian symmetric structure of the type which are defined on bundles associated to the reducible but undecomposable representation of the parabolic subgroup of the Lie group . One example of an operator of this type is the Penrose’s local twistor transport. In this part general theory is presented, and conformally invariant operators are studied in more...
Spectra of Compact Locally Symmetric Manifolds of Negative Curvature.
Spectra of manifolds with small handles.
Spectral analysis of non-compact manifolds using commutator methods
Spectral analysis on singular spaces
Spectral and scattering theory for symbolic potentials of order zero
Spectral Asymmetrie and Zeta Functions.
Spectral asymptotics for manifolds with cylindrical ends
The spectrum of the Laplacian on manifolds with cylindrical ends consists of continuous spectrum of locally finite multiplicity and embedded eigenvalues. We prove a Weyl-type asymptotic formula for the sum of the number of embedded eigenvalues and the scattering phase. In particular, we obtain the optimal upper bound on the number of embedded eigenvalues less than or equal to , where is the dimension of the manifold.
Spectral asymptotics of Laplace operators on surfaces with cusps.
Spectral estimates for Schrödinger and Dirac-type operators on Riemannian manifolds.
Spectral geometry and scattering theory for certain complete surfaces of finite volume.
Spectral Geometry and the Kaehler Condition for Complex Manifolds.
Spectral Geometry for Certain Noncompact Riemannian Manifolds.
Spectral Geometry of Compact Hermitian Symmetric Submanifolds.
Spectral geometry of harmonic maps into warped product manifolds. II.
Spectral geometry of semi-algebraic sets
The spectrum of the Laplace operator on algebraic and semialgebraic subsets in is studied and the number of small eigenvalues is estimated by the degree of .
Spectral invariant of the zeta function of the Laplacian on
Spectral isolation of bi-invariant metrics on compact Lie groups
We show that a bi-invariant metric on a compact connected Lie group is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric on there is a positive integer such that, within a neighborhood of in the class of left-invariant metrics of at most the same volume, is uniquely determined by the first distinct non-zero eigenvalues of its Laplacian (ignoring multiplicities). In the case where is simple, can be chosen to be two....
Spectral resonances for the Laplace-Beltrami operator