Related papers: Isoresonant complex-valued potentials and symmetri…

A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point is radial. Flat and rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for…

We construct a surface with a cylindrical end which has a finite number of Laplace eigenvalues embedded in its continuous spectrum. The surface is obtained by attaching a cylindrical end to a hyperbolic torus with a hole. To our knowledge,…

We describe a method for the accurate calculation of bound-state and resonance energies for one-dimensional potentials. We calculate the shape resonances for symmetric two-barrier potentials and compare them with those coming from the…

Hitherto, a finitely thick barrier next to a well or a rigid wall has been considered the potential of simplest shape giving rise to resonances (metastable states) in one dimension: $x \in(-\infty, \infty)$. In such a potential, there are…

The hyperdeterminant of a polynomial (interpreted as a symmetric tensor) factors into several irreducible factors with multiplicities. Using geometric techniques these factors are identified along with their degrees and their…

Given a sequence of regular finite coverings of complete Riemannian manifolds, we consider the covering solenoid associated with the sequence. We study the leaf-wise Laplacian on the covering solenoid. The main result is that the spectrum…

For manifolds Euclidian at infinity and compact perturbations of the Laplacian, we show that under assumptions involving hyperbolicity of the classical flow on the trapped set and its period spectrum, there are strips below the real axis…

We consider a semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential. The reaction term is a Carath\'eodory function which is resonant with respect to any nonprincipal eigenvalue both at $\pm \infty$ and…

We study the multi-dimensional persistence of Carlsson and Zomorodian and obtain a finer classification based upon the higher tor-modules of a persistence module. We propose a variety structure on the set of isomorphism classes of these…

We study the regularized determinant of the Laplacian as a functional on the space of Mandelstam diagrams (noncompact translation surfaces glued from finite and semi-infinite cylinders). A Mandelstam diagram can be considered as a compact…

Following an idea of Nigel Higson, we develop a method for proving the existence of a meromor-phic continuation for some spectral zeta functions. The method is based on algebras of generalized differential operators. The main theorem…

A 3-dimensional Riemannian manifold equipped with a tensor structure of type $(1,1)$, whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e., these structures…

Compact polyhedral surfaces (or, equivalently, compact Riemann surfaces with conformal flat conical metrics) of an arbitrary genus are considered. After giving a short self-contained survey of their basic spectral properties, we study the…

The existence of a novel enlarged shape invariance property valid for some rational extensions of shape-invariant conventional potentials, first pointed out in the case of the Morse potential, is confirmed by deriving all rational…

We consider almost Einstein solitons $(V,\lambda)$ in a Riemannian manifold when $V$ is a gradient, a solenoidal or a concircular vector field. We explicitly express the function $\lambda$ by means of the gradient vector field $V$ and…

Irreducible bilinear tensorial concomitants of an arbitrary complex antisymmetric valence-2 tensor are derived in four-dimensional spacetime. In addition these bilinear concomitants are symmetric (or antisymmetric), self-dual (or…

We prove semi-classical resolvent estimates for the Schr{\"o}dinger operator with a real-valued L $\infty$ potential on non-compact, connected Riemannian manifolds which may have a compact smooth boundary. We show that the resolvent bound…

A Riemannian orbifold is a mildly singular generalization of a Riemannian manifold which is locally modeled on the quotient of a connected, open manifold under a finite group of isometries. If all of the isometries used to define the local…

We introduce a new kind of Riemannian manifold that includes weakly-, pseudo- and pseudo projective- Ricci symmetric manifolds. The manifold is defined through a generalization of the so called Z tensor; it is named "weakly Z symmetric" and…

In this paper we define a symmetric zeta function. We show that it can be analytically continued to a meromorphic function on $\mathbb{C}^3$ with only simple poles at some special hyperplanes. We also calculate the value of a multiple…