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Displaying similar documents to “Rigidity and L 2 cohomology of hyperbolic manifolds”

Vanishing of the first reduced cohomology with values in an L p -representation

Romain Tessera (2009)

Annales de l’institut Fourier

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We prove that the first reduced cohomology with values in a mixing L p -representation, 1 < p < ∞ , vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced ℓ p -cohomology. As a byproduct, we prove a conjecture by Pansu. Namely, the first reduced L p -cohomology on homogeneous, closed at infinity, Riemannian manifolds vanishes....

Local coordinates for SL ( n , C ) -character varieties of finite-volume hyperbolic 3-manifolds

Pere Menal-Ferrer, Joan Porti (2012)

Annales mathématiques Blaise Pascal

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Given a finite-volume hyperbolic 3-manifold, we compose a lift of the holonomy in SL ( 2 , C ) with the n -dimensional irreducible representation of SL ( 2 , C ) in SL ( n , C ) . In this paper we give local coordinates of the SL ( n , C ) -character variety around the character of this representation. As a corollary, this representation is isolated among all representations that are unipotent at the cusps.

Shadow lemma on the product of Hadamard manifolds and applications

Françoise Dal’Bo, Inkang Kim (2006-2007)

Séminaire de théorie spectrale et géométrie

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In this paper we analyze the limit set of nonelementary subgroups acting by isometries on the product of two pinched Hadamard manifolds. Following M. Burger’s and P. Albuquerque’s works, we study the properties of Patterson-Sullivan’s measures on the limit sets of graph groups associated to convex cocompact groups.

Harmonic maps and representations of non-uniform lattices of PU ( m , 1 )

Vincent Koziarz, Julien Maubon (2008)

Annales de l’institut Fourier

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We study representations of lattices of PU ( m , 1 ) into PU ( n , 1 ) . We show that if a representation is reductive and if m is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic m -space to complex hyperbolic n -space. This allows us to give a differential geometric proof of rigidity results obtained by M. Burger and A. Iozzi. We also define a new invariant associated to representations into PU ( n , 1 ) of non-uniform lattices in PU ( 1 , 1 ) , and more generally of fundamental groups...

Geometric optics expansions with amplification for hyperbolic boundary value problems: Linear problems

Jean-François Coulombel, Olivier Guès (2010)

Annales de l’institut Fourier

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We compute and justify rigorous geometric optics expansions for linear hyperbolic boundary value problems that do not satisfy the uniform Lopatinskii condition. We exhibit an amplification phenomenon for the reflection of small high frequency oscillations at the boundary. Our analysis has two important consequences for such hyperbolic boundary value problems. Firstly, we make precise the optimal energy estimate in Sobolev spaces showing that losses of derivatives must occur from the...