منابع مشابه
Weighted L2 Cohomology of Asymptotically Hyperbolic Manifolds
The main results are summarized by Figure 1. They demonstrate the resiliency of the isomorphism constructed in [Nai99] between weighted cohomology and a variant of weighted L2 cohomology. Our attention is restricted from generic locally symmetric spaces to spaces whose ends are hyperbolic, diffeomorphic to (0,∞) × (S1)n−1, and carry exponentially warped product metrics. For weighting functions ...
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Let (M, g) be a complete, noncompact Riemannian manifold of finite volume. For w : M → (0,∞) a weighting function, the w weighted unreduced L2 cohomology is defined as the usual unreduced L2 cohomology except that dvol is replaced by the measure w dvol. This paper proves that in the case M = Γ\G/K is a locally symmetric space of nonpositive sectional curvature and arbitrary rank whereupon w(m) ...
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A weighted L space on a Riemannian manifold M is obtained by replacing the volume measure dm by a measure of the form φdm, where φ is a positive function referred to as a weight function. If M is noncompact and φ is sufficiently unbounded above or below, the domains of differential operators on these spaces may differ from those on the standard L space. The use of such spaces in connection with...
متن کاملFirst Cohomology on Weighted Semigroup Algebras
The aim of this work is to generalize Johnson’s techniques in order to apply them to establish a bijective correspondence between S-derivations and continuous derivations on Ma(S, ω), where S is a locally compact foundation semigroup with identity e, and ω is a weight function on S, and apply it to find a necessary condition for amenability of weighted group algebras.
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We prove a vanishing theorem for a convex cocompact hyperbolic manifold which relates its L2-cohomology and the Hausdorff dimension of its limit set. The borderline case is shown to characterize the manifold completely.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2007
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-07-08920-4