Related papers: Twisted isospectrality, homological wideness and i…

We study the existence of $L^2$ holomorphic sections of invariant line bundles over Galois coverings of Zariski open sets in Moishezon manilolds. We show that the von Neuman dimension of the space of $L^2$ holomorphic sections is bounded…

A general approach to proving that the length spectrum of a compact Riemannian manifold is an invariant of the Laplace spectrum comes from considering the wave trace, a spectrally determined tempered distribution. The Poisson relation…

We review boundary rigidity theorems assessing that, under appropriate conditions, Riemannian manifolds with the same spectrum of boundary geodesics are isometric. We show how to apply these theorems to the problem of reconstructing a $d+1$…

We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous manifold with a 4-dimensional isometry group. The condition is expressed in terms of…

Substatic Riemannian manifolds with minimal boundary arise naturally in General Relativity as spatial slices of static spacetimes satisfying the Null Energy Condition. Moreover, they constitute a vast generalization of nonnegative Ricci…

We prove the following to results: (1) A subgroup G of the isometry group of a Riemannian manifold M acts properly on M if and only if G is closed in the isometry group of M. (2) The orbits of an isometric action are closed if and only if…

Two Riemannian manifolds are said to be isospectral if the associated Laplace-Belttrami operators have the same eigenvalue spectrum. If the manifolds have boundary, one specifies DIrichlet or Neumann isospectrality depending on the boundary…

We investigate the finiteness structure of a complete non-compact $n$-dimensional Riemannian manifold $M$ whose radial curvature at a base point of $M$ is bounded from below by that of a non-compact von Mangoldt surface of revolution with…

We study in this paper previously defined by V.N. Berestovskii and C.P. Plaut $\delta$-homogeneous spaces in the case of Riemannian manifolds. Every such manifold has non-negative sectional curvature. The universal covering of any…

In this work, we find an equation that relates the Ricci curvature of a riemannian manifold $M$ and the second fundamental forms of two orthogonal foliations of complementary dimensions, $\mathcal{F}$ and $\mathcal{F}^{\bot}$, defined on…

We identify the smooth metrics $\mc{M}(M)$ on a manifold $M^n$ with the smooth isometric embeddings $f_g: (M,g) \rightarrow (\mb{S}^{\tn}, \tg)$ into a standard sphere of large dimension $\tn=\tn(n)$, and their Palais isotopic deformations,…

We study complete, connected and simply connected $n$-dim Riemannian manifold $M$ satisfying Ricci curvature lower bound. Further more, suppose that $M$ admits discrete isometric group actions $G$ so that the diameter of the quotient space…

We establish an integral inequality for the Ricci curvature of a certain class of warped products $M\times_fN$, where the equality holds if and only if it is simply a Riemannian product. We also give a sufficient condition for the…

We show that a simply connected Riemannian homogeneous space M which admits a totally geodesic hypersurface F is isometric to either (a) the Riemannian product of a space of constant curvature and a homogeneous space, or (b) the warped…

We study the size of the isometry group Isom(M, g) of Riemannian manifolds (M, g) as g varies. For M not admitting a circle action, we show that the order of Isom(M, g) can be universally bounded in terms of the bounds on Ricci curvature,…

Ejiri gave a negative answer to a conjecture of Lichnerowicz concerning Riemannian manifolds with constant scalar curvature admitting an infinitesimal non isometric conformal transformation. With this aim he constructed a warped product of…

Let $\calM_1$ and $\calM_2$ denote two compact hyperbolic manifolds. Assume that the multiplicities of eigenvalues of the Laplacian acting on $L^2(\calM_1)$ and $L^2(\calM_2)$ (respectively, multiplicities of lengths of closed geodesics in…

We prove, as our main theorem, the finiteness of topological type of a complete open Riemannian manifold $M$ with a base point $p \in M$ whose radial curvature at $p$ is bounded from below by that of a non-compact model surface of…

For a complete noncompact connected Riemannian manifold with bounded geometry $M^n$, we prove that the isoperimetric profile function $I_{M^n}$ is a locally $\left(1-\frac{1}{n}\right)$-H\"older continuous function and so in particular it…

We define and study isoparametric submanifolds of general ambient spaces and of arbitrary codimension. In particular we study their behaviour with respect to Riemannian submersions and their lift into a Hilbert space. These results are used…