Related papers: Weakly asymptotically hyperbolic manifolds

We use certain Morse functions to construct conformal metrics such that the eigenvalue vector of modified Schouten tensor belongs to a given cone. As a result, we prove that any Riemannian metric on compact 3-manifolds with boundary is…

We study the prescribed scalar curvature problem, namely finding which function can be obtained as the scalar curvature of a metric in a given conformal class. We deal with the case of asymptotically hyperbolic manifolds and restrict…

We study a class of left-invertible operators which we call weakly concave operators. It includes the class of concave operators and some subclasses of expansive strict $m$-isometries with $m > 2$. We prove a Wold-type decomposition for…

A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size. This is a huge class of important…

We consider inverse curvature flows in the $(n+1)$-dimensional Euclidean space, $n\geq 2,$ expanding by arbitrary negative powers of a 1-homogeneous, monotone curvature function $F$ with some concavity properties. We obtain asymptotical…

In this work, we study the asymptotic geometry of the mapping class group and Teichmueller space. We introduce tools for analyzing the geometry of `projection' maps from these spaces to curve complexes of subsurfaces; from this we obtain…

On R^n endowed with a riemannian metric of bounded nonpositive curvature, the weakly convex closed subsets are topologically trivial. The stability of such subsets under intersection characterizes the euclidean spaces.

We introduce new metric structures on a smooth manifold (called "weak" structures) that generalize the almost contact, Sasakian, cosymplectic, etc. metric structures $(\varphi,\xi,\eta,g)$ and allow us to take a fresh look at the classical…

We study a very general class of first-order linear hyperbolic systems that both become weakly hyperbolic and contain lower-order coefficients that blow up at a single time $t = 0$. In "critical" weakly hyperbolic settings, it is well-known…

This article investigates the asymptotics of $\rm{G}_2$-monopoles. First, we prove that when the underlying $\rm{G}_2$-manifold is nonparabolic (i.e. admits a positive Green's function), finite intermediate energy monopoles with bounded…

The curvature and the reduced curvature are basic differential invariants of the pair (Hamiltonian system, Lagrange distribution) on the symplectic manifold. It is shown that the negativity of the reduced curvature implies the hyperbolicity…

We consider a class of $\mathcal C^{4}$ partially hyperbolic systems on $\mathbb T^2$ described by maps $F_\varepsilon(x,\theta)=(f(x,\theta),\theta+\varepsilon\omega(x,\theta))$ where $f(\cdot,\theta)$ are expanding maps of the circle. For…

This is a significantly improved version with new applications. We show that there are many cohomogeneity one manifolds which do not admit an analytic invariant metric with non-negative sectional curvature, although they do have a smooth…

A connected Riemannian manifold M has constant vector curvature \epsilon, denoted by cvc(\epsilon), if every tangent vector v in TM lies in a 2-plane with sectional curvature \epsilon. By scaling the metric on M, we can always assume that…

The (measure-theoretical) entropy of a diffeomorphism along an expanding invariant foliation is the rate of complexity generated by the diffeomorphism along the leaves of the foliation. We prove that this number varies upper…

We study deformations of complex hyperbolic surfaces which furnish the simplest examples of: (i) negatively curved K\"ahler manifolds and (ii) negatively curved Riemannian manifolds not having {\it constant} curvature. Although such complex…

A family of non-radial solutions of the Yamabe equation, with reference the hyperbolic space, is constructed using power series. As a result, we obtain a family of asymptotically hyperbolic metrics, with spherical conformal infinity, with…

We consider 3-dimensional hyperbolic cone-manifolds, singular along infinite lines, which are ``convex co-compact'' in a natural sense. We prove an infinitesimal rigidity statement when the angle around the singular lines is less than…

We consider admissible random walks on hyperbolic graphs. For a given harmonic function on such a graph, we prove that asymptotic properties of non-tangential boundedness and non-tangential convergence are almost everywhere equivalent. The…

We consider weak solutions for the obstacle-type viscoelastic ($\nu>0$) and very weak solutions for the obstacle inviscid ($\nu=0$) Dirichlet problems for the heterogeneous and anisotropic wave equation in a fractional framework based on…