A volume comparison estimate with radially symmetric Ricci curvature lower bound and its applications.
A volume comparison theorem and number of ends for manifolds with asymptotically nonnegative Ricci curvature.
In this paper we establish a volume comparison theorem for cocentric metric balls at arbitrary point for manifolds with asymptotically nonnegative Ricci curvature, which will allow us to prove the finiteness of the number of ends.
Abnormality of trajectory in sub-Riemannian structure
In the sub-Riemannian framework, we give geometric necessary and sufficient conditions for the existence of abnormal extremals of the Maximum Principle. We give relations between abnormality, -rigidity and length minimizing. In particular, in the case of three dimensional manifolds we show that, if there exist abnormal extremals, generically, they are locally length minimizing and in the case of four dimensional manifolds we exhibit abnormal extremals which are not -rigid and which can be minimizing...
About a decomposition of the space of symmetric tensors of compact support on a Riemann manifold.
Actions des groupes de Lie presque simples et positivité de la -courbure
Affine Actions of Higher Rank Lattices.
Affinely equivalent complete flat manifolds
Let E Aff(Γ,G, m) be the set of affine equivalence classes of m-dimensional complete flat manifolds with a fixed fundamental group Γ and a fixed holonomy group G. Let n be the dimension of a closed flat manifold whose fundamental group is isomorphic to Γ. We describe E Aff(Γ,G, m) in terms of equivalence classes of pairs (ε, ρ), consisting of epimorphisms of Γ onto G and representations of G in ℝm-n. As an application we give some estimates of card E Aff(Γ,G, m).
Alexandrov spaces with nonnegative curvature outside a compact set.
Algebraic properties of curvature operators in Lorentzian manifolds with large isometry groups.
Almost invariant submanifolds for compact group actions
We define a distance between submanifolds of a riemannian manifold and show that, if a compact submanifold is not moved too much under the isometric action of a compact group , there is a -invariant submanifold -close to . The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney’s idea of realizing submanifolds as zeros of sections...
Almost-Einstein manifolds with nonnegative isotropic curvature
Let , , be a compact simply-connected Riemannian -manifold with nonnegative isotropic curvature. Given , we prove that there exists satisfying the following: If the scalar curvature of satisfiesand the Einstein tensor satisfiesthen is diffeomorphic to a symmetric space of compact type.This is related to the result of S. Brendle on the metric rigidity of Einstein manifolds with nonnegative isotropic curvature.
Amalgamations of homogeneous Riemannian spaces
Amenable Groups and Stabilizers of Measures on the Boundary of a Hadamard Manifold.
An Eigenvalue Pinching Theorem.
An equivalent flat condition.
An Equivariant Pniching Theorem.
An excess sphere theorem
An existence result for minimal spheres in manifolds boundary
We prove the existence of a not homotopically trivial minimal sphere in a 3-manifold with boundary, obtained by deleting an open connected subset from a compact Riemannian oriented 3-manifold with boundary, having trivial second homotopy group.
An Existence Theorem for Harmonic Maps.
An explicit classification of 3-dimensional Riemannian spaces satisfying