The space of nonpositively curved metrics of a negatively curved manifold
We show that the space of nonpositively curved metrics of a negatively curved manifold is highly non connected.
math.DG↗
arXiv subjects
P. Ontaneda
Publications and source records attributed to P. Ontaneda.
Teichmüller Spaces and Bundles with Negatively Curved Fibers
We study the Teichmüller space of negatively curved metrics on a high dimensional manifold, with applications to bundles with negatively curved fibers.
math.DG↗
On the topology of the space of negatively curved metrics
We show that the space of negatively curved metrics of a closed negatively curved Riemannian $n$-manifold, $n\geq 10$, is highly non-connected.
math.DG↗
On the moduli space of negatively curved metrics of a hyperbolic manifold
We study the moduli space of negatively curved metrics of a hyperbolic manifold.
math.DG↗
The Teichmüller Space of Pinched Negatively Curved Metrics on a Hyperbolic Manifold is not Contractible
For a smooth manifold $M$ we define the Teichmüller space $\cT(M)$ of all Riemannian metrics on $M$ and the Teichmüller space $\cT^ε(M)$ of $ε$-pinched negatively curved metrics on $M$, where $0\leqε\leq\infty$. We prove that if $M$ is hyperbolic the natural inclusion $\cT^ε(M)\hookrightarrow\cT(M)$ is, in general, not homotopically trivial. In particular, $\cT^ε(M)$ is, in general, not contractible.
math.DG↗
On the fixed homogeneous circle problem
We give some results about the dynamics of a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. Our main results concern (1) singularities and (2) the dynamics in the plane that contains the circle. The study presented here is purely analytic.
math.DS↗
On the Existence of Periodic Orbits for the Fixed Homogeneous Circle Problem
We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and very near the homogeneous circle, as well as eight and spiral periodic orbits.
math.CA↗
Continuous Symmetric Perturbations of Planar Power Law Forces
We show the existence of periodic solutions for continuous symmetric perturbations of certain planar power law problems.
math.CA↗
A caveat on the convergence of the Ricci flow for pinched negatively curved manifolds
We give examples of pinched negatively curved manifolds for which the Ricci flow does not converge smoothly.
math.DG↗
Exotic structures and the limitations of certain analytic methods in geometry
In this survey we review some results concerning negatively curved exotic strucutres (DIFF and PL) and its (unexpected) implications on the limitations of some analytic methods in geometry. This article is dedicated to the memory of Armand Borel.
math.DG↗
Branched covers of hyperbolic manifolds and harmonic maps
We give examples of harmonic maps between negatively curved manifolds with special properties. These negatively curved manifolds do not have the homotopy type of a locally symmetric space.
math.DG↗
Cellular harmonic maps which are not diffeomorphisms
We give examples of harmonic cellular maps between negatively curved manifolds which are not diffeomorphisms but are homotopic to diffeomorphisms.
math.DG↗
A formula for the Whitehead group of a three-dimansional crystallographic group
We give an explicit formula for Whitehead group of a three-dimensional crystallographic group in terms of the Whitehead groups of its virtually infinite cyclic subgroups.
math.KT↗