131 research outputs found
Rigidity and cohomology of hyperbolic manifolds
When X=\Gamma\backslash \H^n is a real hyperbolic manifold, it is already
known that if the critical exponent is small enough then some cohomology spaces
and some spaces of harmonic forms vanish. In this paper, we show rigidity
results in the borderline case of these vanishing results
Harmonic Functions On Manifolds Whose Large Sphere Are Small
We study the growth of harmonic functions on complete Riemann-ian manifolds
where the extrinsic diameter of geodesic spheres is sublinear. It is an
generalization of a result of A. Kazue. We also get a Cheng and Yau estimates
for the gradient of harmonic functions
Riesz transform on manifolds with quadratic curvature decay
We investigate the -boundness of the Riesz transform on Riemannian
manifolds whose Ricci curvature has quadratic decay. Two criteria for the
-unboundness of the Riesz transform are given. We recover known results
about manifolds that are Euclidean or conical at infinity
Riesz transforms on connected sums
We investigate the boundness of the Riesz transform on for connected
sum of manifolds where the Riesz transform is bounded on
On the differential form spectrum of hyperbolic manifolds
We give a lower bound for the bottom of the differential form spectrum
on hyperbolic manifolds, generalizing thus a well-known result due to Sullivan
and Corlette in the function case. Our method is based on the study of the
resolvent associated with the Hodge-de Rham Laplacian and leads to applications
for the (co)homology and topology of certain classes of hyperbolic manifolds
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