相关论文: Lp-cohomology of negatively curved manifolds

We compute the space of $L^2$ harmonic forms (outside the middle degrees) on negatively curved Kaehler manifolds of finite volume.

A sharp vanishing theorem for the $L^p$ cohomology torsion of Riemannian manifolds with pinched negative curvature is given. It follows that certain negatively curved homogeneous spaces cannot be quasiisometric to better pinched manifolds.

We prove a non-vanishing result for the $L_{q,p}$-cohomology of complete simply-connected Riemannian manifolds with pinched negative curvature.

We give a topological interpretation of the space of L2-harmonic forms on finite-volume manifolds with sufficiently pinched negative curvature. We give examples showing that this interpretation fails if the curvature is not sufficiently…

The $L^p$-cohomology in degree 1 of Riemannian homogeneous spaces is computed. It turns out that reduced cohomology does not vanish exactly for spaces quasiisometric to negatively curved homogeneous spaces.

Let $(M,g)$ be an incomplete Riemannian manifold of finite volume and let $2\leq p<\infty$. In the first part of this paper we prove that under certain assumptions the inclusion of the space of $L^p$-differential forms into that of…

We survey several notions of entropy related to a compact manifold of negative curvature, some relations between them, and the rigidity problems.

This is a short survey of Riemannian geometric applications of Lp-cohomology of thick spaces, p not equal to 2.

In this note we describe basic geometric properties of p-harmonic forms and p-coclosed forms and use them to reprove vanishing theorems of Pansu and new injectivity theorems for the Lp -cohomology of simply connected, pinched negatively…

We study some relation between some geometrically defined classes of diffeomorphisms between manifolds and the $L_{q,p}$-cohomology of these manifolds. Some applications to vanishing and non vanishing results in $L_{q,p}$-cohomology are…

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.

We give a simple construction of new, complete, finite volume manifolds $M$ of bounded, nonpositive curvature. These manifolds have ends that look like a mixture of locally symmetric ends of different ranks and their fundamental groups are…

We calculate the rational equivariant cohomology of the spaces of non-contractible loops in compact space forms and show how to apply these calculations for proving the existence of closed geodesics.

Conformal invariants of manifolds of non-positive scalar curvature are studied in association with growth in volume and fundamental group.

This article surveys results for Riemannian manifolds of positive and non-negative sectional curvature with symmetries.

Let $M$ be a closed complex submanifold in ${\mathbb C}^N$ with the complete K\"ahler metric induced by the Euclidean metric. Several finiteness theorems on the $L^p$ Bergman space of holomorphic sections of a given Hermitian line bundle…

We investigate the topology and geometry of compact submanifolds in space forms of nonnegative curvature that satisfy a lower bound on the sectional curvature, depending only on the length of the mean curvature vector of the immersion. We…

This is a survey on known results and open problems about Smooth and PL-Rigidity Problem for negatively curved locally symmetric spaces. We also review some developments about studying the basic topological properties of the space of…

We study noncompact, complete, finite volume, negatively curved manifolds $M$. We construct $M$ with infinitely generated fundamental groups in all dimensions $n \geq 2$. We construct $M$ whose cusp cross sections are compact hyperbolic…

We construct several infinite families of nonnegatively curved manifolds of low cohomogeneity and small dimension which can be distinguished by their cohomology rings. In particular, we exhibit an infinite family of eight-dimensional…