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On the growth of nonuniform lattices in pinched negatively curved manifolds  [PDF]
Fran?oise Dal'Bo,Marc Peigné,Jean-Claude Picaud,Andrea Sambusetti
Mathematics , 2009, DOI: 10.1515/CRELLE.2009.010
Abstract: We study the relation between the exponential growth rate of volume in a pinched negatively curved manifold and the critical exponent of its lattices. These objects have a long and interesting story and are closely related to the geometry and the dynamical properties of the geodesic flow of the manifold .
A caveat on the convergence of the Ricci flow for pinched negatively curved manifolds  [PDF]
F. T. Farrell,P. Ontaneda
Mathematics , 2003,
Abstract: We give examples of pinched negatively curved manifolds for which the Ricci flow does not converge smoothly.
The Teichmüller Space of Pinched Negatively Curved Metrics on a Hyperbolic Manifold is not Contractible  [PDF]
F. T. Farrell,P. Ontaneda
Mathematics , 2004,
Abstract: For a smooth manifold $M$ we define the Teichm\"uller space $\cT(M)$ of all Riemannian metrics on $M$ and the Teichm\"uller space $\cT^\epsilon(M)$ of $\epsilon$-pinched negatively curved metrics on $M$, where $0\leq\epsilon\leq\infty$. We prove that if $M$ is hyperbolic the natural inclusion $\cT^\epsilon(M)\hookrightarrow\cT(M)$ is, in general, not homotopically trivial. In particular, $\cT^\epsilon(M)$ is, in general, not contractible.
Complete negatively curved immersed ends in $\Bbb R^3$  [PDF]
Sérgio Mendon?a
Mathematics , 2014,
Abstract: This paper extends, in a sharp way, the famous Efimov's Theorem to immersed ends in $\real^3$. More precisely, let $M$ be a non-compact connected surface with compact boundary. Then there is no complete isometric immersion of $M$ into $\Bbb R^3$ satisfying that $\int_M |K|=+\infty$ and $K\le-\kappa<0$, where $\kappa$ is a positive constant and $K$ is the Gaussian curvature of $M$. In particular Efimov's Theorem holds for complete Hadamard immersed surfaces, whose Gaussian curvature $K$ is bounded away from zero outside a compact set.
Classification of negatively pinched manifolds with amenable fundamental groups  [PDF]
Igor Belegradek,Vitali Kapovitch
Mathematics , 2004,
Abstract: We give a diffeomorphism classification of pinched negatively curved manifolds with amenable fundamental groups, namely, they are precisely the M\"obius band, and the products of a line with the total spaces of flat vector bundles over closed infranilmanifolds.
On the topology of the space of negatively curved metrics  [PDF]
F. T. Farrell,P. Ontaneda
Mathematics , 2006,
Abstract: We show that the space of negatively curved metrics of a closed negatively curved Riemannian $n$-manifold, $n\geq 10$, is highly non-connected.
The space of nonpositively curved metrics of a negatively curved manifold  [PDF]
F. T. Farrell,P. Ontaneda
Mathematics , 2011,
Abstract: We show that the space of nonpositively curved metrics of a negatively curved manifold is highly non connected.
Teichmüller Spaces and Bundles with Negatively Curved Fibers  [PDF]
F. T. Farrell,P. Ontaneda
Mathematics , 2007,
Abstract: We study the Teichm\"uller space of negatively curved metrics on a high dimensional manifold, with applications to bundles with negatively curved fibers.
On the moduli space of negatively curved metrics of a hyperbolic manifold  [PDF]
F. T. Farrell,P. Ontaneda
Mathematics , 2008, DOI: 10.1112/jtopol/jtq016
Abstract: We study the moduli space of negatively curved metrics of a hyperbolic manifold.
Lp-cohomology of negatively curved manifolds  [PDF]
Nader Yeganefar
Mathematics , 2004, DOI: 10.1007/BF02384790
Abstract: We compute the $L^p$-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds.
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