Related papers: On the spectrum of the Laplace-Beltrami operator f…
We discuss the essential spectrum of essentially self-adjoint elliptic differential operators of first order and of Laplace type operators on Riemannian vector bundles over geometrically finite orbifolds.
We introduce and study {\it new} relative spectral invariants of {\it two} elliptic partial differential operators of Laplace and Dirac type on compact smooth manifolds without boundary that depend on both the eigenvalues and the…
We derive an explicit formula for the Laplace-Beltrami operator on the orthogonal Stiefel manifold, viewed as a constraint submanifold of the Euclidean space of real matrices equipped with the Frobenius metric. Using the general framework…
We establish criteria for the stability of the essential spectrum for unbounded operators acting in Banach modules. The applications cover operators acting on sections of vector fiber bundles over non-smooth manifolds or locally compact…
We establish two-term spectral asymptotics for the operator of linear elasticity with mixed boundary conditions on a smooth compact Riemannian manifold of arbitrary dimension. We illustrate our results by explicit examples in dimension two…
Eigendecomposition of the Laplace-Beltrami operator is instrumental for a variety of applications from physics to data science. We develop a numerical method of computation of the eigenvalues and eigenfunctions of the Laplace-Beltrami…
A class of conformal deformations of Rindler-like spaces is analyzed. We study the spectral properties of the Laplace operators associated with $p-$forms and acting in these spaces and in their spatial sections. The spectral density of…
In this paper we introduce a notion of scattering theory for the Laplace-Beltrami operator on non-compact, connected and complete Riemannian manifolds. A principal condition is given by a certain positive lower bound of the second…
The functional determinant of Laplace-type operators on the 3-dimensional non-compact hyperbolic manifold with invariant fundamental domain of finite volume is computed by quadratures and making use of the related terms of the Selberg trace…
This paper relates the spectrum of the scalar Laplacian of an asymptotically hyperbolic Einstein metric to the conformal geometry of its ``ideal boundary'' at infinity. It follows from work of R. Mazzeo that the essential spectrum of such a…
We consider the Laplace-Beltrami operator in tubular neighbourhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the…
We study spectral asymptotics for the Laplace operator on differential forms on a Riemannian foliated manifold equipped with a bundle-like metric in the case when the metric is blown up in directions normal to the leaves of the foliation.…
In this paper we study the asymptotic behavior of second-order uniformly elliptic operators on weighted Riemannian manifolds. They naturally emerge when studying spectral properties of the Laplace-Beltrami operator on families of manifolds…
We obtain an asymptotic formula for the spectrum distribution function of the Laplace operator on a compact Riemannian Sol-manifold in the adiabatic limit determined by a one-dimensional foliation defined by the orbits of a left-invariant…
We study harmonic functions for the Laplace-Beltrami operator on the real hyperbolic ball. We obtain necessary and sufficient conditions for this functions and their normal derivatives to have a boundary distribution.In doing so, we put…
We present a numerical algorithm for computing the spectrum of the Laplace-de Rham operator on Calabi-Yau manifolds, extending previous work on the scalar Laplace operator. Using an approximate Calabi-Yau metric as input, we compute the…
Let $P$ be an operator of Dirac type on a compact Riemannian manifold with smooth boundary. We impose spectral boundary conditions and study the asymptotics of the heat trace of the associated operator of Laplace type.
Let $P$ be an operator of Dirac type on a compact Riemannian manifold with smooth boundary. We impose spectral boundary conditions and study the asymptotics of the heat trace of the associated operator of Laplace type.
We study Laplace-type operators on hybrid manifolds, i.e. on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace-Beltrami operators on each…
We constrain the low-energy spectra of Laplace operators on closed hyperbolic manifolds and orbifolds in three dimensions, including the standard Laplace-Beltrami operator on functions and the Laplacian on powers of the cotangent bundle.…