Related papers: Spectral properties of 4-dimensional compact flat …

Through exploring the embedded transnormal systems of codimension 1, we show the existence of a transnormal function on a connected complete Riemannian manifold requires the underlying manifold to have a vector bundle structure or a linear…

A number of questions related to the length spectrum of surfaces are discussed and in particular the existence of pairs of surfaces which though not isometric are isospectral. Here by isospectral we mean that a pair of bodies have the same…

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.…

Compact flat surfaces of homogeneous Riemannian 3-manifolds with isometry group of dimension 4 are classified. Non-existence results for compact constant Gauss curvature surfaces in these 3-manifolds are established.

Bond-percolation graphs are random subgraphs of the d-dimensional integer lattice generated by a standard bond-percolation process. The associated graph Laplacians, subject to Dirichlet or Neumann conditions at cluster boundaries, represent…

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…

Let $M$ be a $2m$-dimensional compact Riemannian manifold. We show that the spectrum of the Hodge Laplacian acting on $m$-forms does not determine whether the manifold has boundary, nor does it determine the lengths of the closed geodesics.…

Let $(M,g)$ be a surface with Riemannian metric and curved conic singularities. More precisely, a neighbourhood of a singularity is isometric to $(0,1)\times S^1$ with metric $g_{\text{conic}}=dr^2+f(r)^2d\theta^2, r\in(0,1)$. We study the…

We characteristize those Einstein four manifolds which are locally symmetric spaces of noncompact type. Namely they are four manifolds which admit solutions to the (non-Abelian) Seiberg Witten equations and satisty certain characterisitc…

We study two types of isotropic planes: weakly isotropic and strongly isotropic planes. We prove that a Riemannian manifold of indefinite metric is conformally flat if and only if its curvature tensor vanishes on all the strongly isotropic…

We consider the spectrum of the Laplace operator acting on $\mathcal{L}^p$ over a conformally compact manifold for $1 \leq p \leq \infty$. We prove that for $p \neq 2$ this spectrum always contains an open region of the complex plane. We…

We prove that every locally conformally flat metric on a closed, oriented hyperbolic 4-manifold with scalar curvature bounded below by -12 satisfies Schoen's conjecture. We also classify all closed Riemannian 4-manifolds of positive scalar…

We construct spectral triples in a sense of noncommutative differential geometry, associated with a Riemannian foliation on a compact manifold, and describe its dimension spectrum.

In this paper are given explicit calculations of Laplace operator spectrum for smooth real/complex-valued functions on all connected compact simple rank three Lie groups with biinvariant Riemannian metric and established a connection of…

We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. For a given number $N$ we construct periodic (i.e. covering) manifolds such that the essential spectrum of the corresponding…

\.{Z}uk proved that if a finitely generated group admits a Cayley graph such that the Laplacian on the links of this Cayley graph has a spectral gap $> \frac{1}{2}$, then the group has property (T), or equivalently, every affine isometric…

We show that on a closed Riemannian manifold with fundamental group isomorphic to $\mathbb{Z}$, other than the circle, every isometry that is homotopic to the identity possesses infinitely many invariant geodesics. This completes a recent…

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…

The main aim of this paper is the description of a large class of lattices in some nilpotent Lie groups, sometimes filiformes, carrying a flat left invariant linear connection anf often a left invariant symplectic form. As a consequence we…

Let \((M^n,g)\) be a smooth closed Riemannian manifold of dimension \(n \ge 5\) with positive Yamabe invariant and semi-positive \(Q\)-curvature. We establish a precompactness result in the \(C^{\alpha}\)-H\"older topologie on the space of…