Title Geometric and spectral analysis / Pierre Albin, Dmitry Jakobson, Frederic Rochon, editors

Published Providence, Rhode Island ; Montréal, Québec : American Mathematical Society : Centre de Recherches Mathematiques, 2014 ©2014

Click on the following:
ProQuest Ebook Central

Copies

Description 1 online resource (378 pages) : illustrations Series Contemporary Mathematics. Centre de Recherches Mathématiques Proceedings, 1098-3627 ; 613 Contemporary mathematics (American Mathematical Society). Centre de recherches mathématiques proceedings ; 613. Contents Cover -- Title page -- Contents -- Preface -- A New Proof of a Bismut-Zhang Formula for Some Class of Representations -- 1. Introduction -- 2. The idea of the proof -- 3. The Milnor metric and the Farber-Turaev torsion -- 4. The Ray-Singer norm of the Refined Analytic Torsion -- 5. The Determinant Line Bundle over the Space of Representations -- 6. The Bismut-Zhang theorem for some non-unitary representations -- References -- Tunneling, the Quillen Metric and Analytic Torsion for High Powers of a Holomorphic Line Bundle -- 1. Introduction ""2. Proofs of the main results""""3. Further remarks on tunneling and outlook""; ""References""; ""Simple Spectrum and Rayleigh Quotients""; ""1. Introduction""; ""2. The Conformal class""; ""3. The KÃ?hler class""; ""Acknowledgments""; ""References""; ""Smooth and Singular KÃ?hlerâ€?Einstein Metrics""; ""1. Introduction""; ""2. The \KE equation""; ""3. \K edge geometry""; ""4. Existence and non-existence""; ""5. Energy functionals""; ""6. The Ricci continuity method""; ""7. A priori estimates for Mongeâ€?AmpÃ?re equations""; ""8. The asymptotically logarithmic world"" 9. The logarithmic Calabi problemAcknowledgements -- References -- Complex -Manifolds -- 1. Introduction -- 2. Complex -structures -- 3. Holomorphic vector bundles -- 4. The boundary of a complex -manifold -- 5. Local invariants -- 6. Indicial complexes -- 7. Underlying CR complexes -- 8. Spectrum -- 9. Indicial cohomology -- Appendix A. Totally characteristic differential operators -- References -- Iterative Structures on Singular Manifolds -- Introduction -- 1. Manifolds with singularities of higher order -- 2. The cone algebra 3. The edge algebra4. Shapiro-Lopatinskij edge-ellipticity -- 5. Iterated Mellin quantisation -- 6. Toeplitz edge problems -- References -- The Fundamental Gap and One-Dimensional Collapse -- 1. Motivation and results -- 2. Collapsing triangular domains -- 3. Collapsing polygonal domains -- 4. The general case -- Acknowledgements -- References -- The Logarithmic Singularities of the Green Functions of the Conformal Powers of the Laplacian -- Introduction -- 1. The Heat Kernel of the Laplace Operator -- 2. The Bergman Kernel of a Strictly Pseudoconvex Domain 3. Ambient Metric and Conformal Powers of the Laplacian4. Local Conformal Invariants -- 5. Scattering Theory and Conformal Fractional Powers of the Laplacian -- 6. Green Functions of Elliptic Operators -- 7. Green Functions and Conformal Geometry -- 8. Proof of Theorem 7.3 -- References -- A Symbolic Calculus for Fourier Integral Operators -- Introduction -- 1. Notation and definitions -- 2. Canonical transformations in * -- 3. Fourier integral operators -- 4. Symbolic calculus for FIOs -- References -- Strichartz Estimates on Exterior Polygonal Domains Notes "CRM Workshops on: Geometry of Eigenvalues and Eigenfunctions, June 4-8, 2012, Manifolds of Metrics and Probabilistic Methods in Geometry and Analysis, July 2-6, 2012, Spectral Invariants on Non-compact and Singular Spaces, July 23-27, 2012, Centre de Recherches Mathematiques, University de Montreal, Montreal, Quebec, Canada."--Cover Bibliography Includes bibliographical references at the end of each chapters Notes Print version record Subject Spectrum analysis -- Congresses Geometric analysis -- Congresses Geometric analysis. Spectrum analysis. Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Elliptic equations on manifolds, general theory. Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Pseudodifferential and Fourier integral operators on manifolds. Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Spectral problems; spectral geometry; scattering theory. Global analysis, analysis on manifolds -- Partial differential equations on manifolds; differential operators -- Determinants and determinant bundles, analytic torsion. Probability theory and stochastic processes -- Geometric probability and stochastic geometry -- Geometric probability and stochastic geometry. Calculus of variations and optimal control; optimization -- Variational methods for eigenvalues of operators -- Variational methods for eigenvalues of operators. Functional analysis -- Linear function spaces and their duals -- Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems. Differential geometry -- Classical differential geometry -- Conformal differential geometry. Genre/Form Conference papers and proceedings. Form Electronic book Author Albin, Pierre, 1976- editor. Jakobson, Dmitry, 1970- editor. Rochon, Frédéric, 1978- editor. ISBN 9781470420598 1470420597

  Permalink