Using elementary comparison geometry, we prove: Let (M, g) be a simply-connected complete Riemannian manifold of dimension >= 3. Suppose that the sectional curvature K satisfies -1-s(r) <= K <= -1, where r denotes distance to a fixed point in M. If lim(r ->infinity) e(2r) s(r) = 0, then (M, g) has to be isometric to H-n.The same proof also yields that if K satisfies -s(r) <= K <= 0 where lim(r ->infinity) r(2) s(r) = 0, then (M, g) is isometric to R-n, a result due to Greene and Wu.Our second result is a local one: Let (M, g) be any Riemannian manifold. For a E R, if K < a on a geodesic ball Bp (R) in M and K = a on partial derivative B-p (R), then K = a on B-p (R)
Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for man...
It has been known that if a Riemannian manifold admits a non-trivial Riemannian submersion with tota...
Given a smooth, compact manifold, an important question to ask is, what are the best\u27\u27 metric...
Using elementary comparison geometry, we prove: Let (M, g) be a simply-connected complete Riemannian...
Abstract. We prove that a simply-connected complete Riemannian manifold of dimension ≥ 3 whose secti...
. The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersu...
The classical Three Gap Theorem asserts that for n ∈ N and p ∈ R, there are at most three distinct d...
ABSTRACT: Let (Si, gi), i = 1, 2 be two compact riemannian surfaces isometrically embedded in euclid...
33 pages, 1 dessinInternational audienceOne proves the following gap theorem, involving the volume a...
33 pages, 1 dessinInternational audienceOne proves the following gap theorem, involving the volume a...
We construct and use solutions, subsolutions, and supersolutions of differential equa-tions as catal...
In an earlier article we obtain a sharp inequality for an arbitrary isometric immer-sion from a Riem...
Given a smooth, compact manifold, an important question to ask is, what are the ``best\u27\u27 metri...
Abstract. In this paper, we study complete open manifolds with sectional curvature bounded from belo...
Let (M, g) be a compact Ricci-fiat 4-manifold. For p is an element of M let K-max(P) (respectively K...
Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for man...
It has been known that if a Riemannian manifold admits a non-trivial Riemannian submersion with tota...
Given a smooth, compact manifold, an important question to ask is, what are the best\u27\u27 metric...
Using elementary comparison geometry, we prove: Let (M, g) be a simply-connected complete Riemannian...
Abstract. We prove that a simply-connected complete Riemannian manifold of dimension ≥ 3 whose secti...
. The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersu...
The classical Three Gap Theorem asserts that for n ∈ N and p ∈ R, there are at most three distinct d...
ABSTRACT: Let (Si, gi), i = 1, 2 be two compact riemannian surfaces isometrically embedded in euclid...
33 pages, 1 dessinInternational audienceOne proves the following gap theorem, involving the volume a...
33 pages, 1 dessinInternational audienceOne proves the following gap theorem, involving the volume a...
We construct and use solutions, subsolutions, and supersolutions of differential equa-tions as catal...
In an earlier article we obtain a sharp inequality for an arbitrary isometric immer-sion from a Riem...
Given a smooth, compact manifold, an important question to ask is, what are the ``best\u27\u27 metri...
Abstract. In this paper, we study complete open manifolds with sectional curvature bounded from belo...
Let (M, g) be a compact Ricci-fiat 4-manifold. For p is an element of M let K-max(P) (respectively K...
Unpublished results of S Straus and W Browder state that two notions of homotopy equivalence for man...
It has been known that if a Riemannian manifold admits a non-trivial Riemannian submersion with tota...
Given a smooth, compact manifold, an important question to ask is, what are the best\u27\u27 metric...