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Analysis on Manifolds with Generalized Cusps


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  • Product Description

In this book we are interested in manifolds with cusp like singularities that are in between the cases of cylindrical end and of hyperbolic cusp. More precisely, we study the Laplace operator acting on p-forms, defined on an n-dimensional manifold with generalized cusp. Such a manifold consists of a compact piece and a noncompact one. The noncompact piece is isometric to the generalized cusp. A generalized cusp is an n-dimensional noncompact manifold equipped with a parameter dependent warped product metric. When the positive parameter goes to zero, the cusp becomes a cylinder, and when it goes to infinity, it could be thought of as approaching the n-dimensional hyperbolic cusp. In such a manifold we construct the generalized eigenforms of the Laplacian. Thus, we give a description of the continuous spectral decomposition of the Laplace operator and we determine some of its important properties, like analyticity and the existence of a functional equation. We also define the stationary scattering matrix and find its analytic properties and its functional equation.

Product Specifications
SKU :COC27864
AuthorNikolaos Roidos
Number of Pages96
Publishing Year2010-12-09T00:00:00.000
Edition1 st
Book TypeReal analysis, real variables
Country of Manufacture
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-07-29 00:00:00