Geometric and Spectral Analysis

In 2012, the Centre de Recherches Mathematiques was at the center of many interesting developments in geometric and spectral analysis, with a thematic program on Geometric Analysis and Spectral Theory followed by a thematic year on Moduli Spaces, Extremality and Global Invariants.This volume contain...

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Main Authors: Albin, Pierre, Jakobson, Dmitry, Rochon, Frédéric, Workshop on Geometry of Eigenvalues and Eigenfunctions, Workshop on Manifolds of Metrics and Probabilistic Methods in Geometry, Workshop "Spectral Invariants on Non-compact and Singular Spaces"
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 03.12.2014
Centre de Recherches Mathematiques
Centre de Recherches Mathématiques
Edition:1
Series:Contemporary Mathematics
Subjects:
Congresses
Geometric analysis
Geometric analysis > Congresses
Spectrum analysis
Spectrum analysis > Congresses
ISBN:9781470410438, 1470410435
ISSN:0271-4132, 1098-3627
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Abstract In 2012, the Centre de Recherches Mathematiques was at the center of many interesting developments in geometric and spectral analysis, with a thematic program on Geometric Analysis and Spectral Theory followed by a thematic year on Moduli Spaces, Extremality and Global Invariants.This volume contains original contributions as well as useful survey articles of recent developments by participants from three of the workshops organized during these programs: Geometry of Eigenvalues and Eigenfunctions, held from June 4-8, 2012; Manifolds of Metrics and Probabilistic Methods in Geometry and Analysis, held from July 2-6, 2012; and Spectral Invariants on Non-compact and Singular Spaces, held from July 23-27, 2012.The topics covered in this volume include Fourier integral operators, eigenfunctions, probability and analysis on singular spaces, complex geometry, Kahler-Einstein metrics, analytic torsion, and Strichartz estimates.
AbstractList In 2012, the Centre de Recherches Mathematiques was at the center of many interesting developments in geometric and spectral analysis, with a thematic program on Geometric Analysis and Spectral Theory followed by a thematic year on Moduli Spaces, Extremality and Global Invariants.This volume contains original contributions as well as useful survey articles of recent developments by participants from three of the workshops organized during these programs: Geometry of Eigenvalues and Eigenfunctions, held from June 4-8, 2012; Manifolds of Metrics and Probabilistic Methods in Geometry and Analysis, held from July 2-6, 2012; and Spectral Invariants on Non-compact and Singular Spaces, held from July 23-27, 2012.The topics covered in this volume include Fourier integral operators, eigenfunctions, probability and analysis on singular spaces, complex geometry, Kahler-Einstein metrics, analytic torsion, and Strichartz estimates.
Author Albin, Pierre
Jakobson, Dmitry
Workshop "Spectral Invariants on Non-compact and Singular Spaces"
Rochon, Frédéric
Workshop on Geometry of Eigenvalues and Eigenfunctions
Workshop on Manifolds of Metrics and Probabilistic Methods in Geometry
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Albin, Pierre
Jakobson, Dmitry
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Notes Includes bibliographical references
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 Mathématiques, Université de Montréal, Quebec, Canada.
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PublicationSeriesTitle Contemporary Mathematics
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Publisher American Mathematical Society
Centre de Recherches Mathematiques
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Snippet In 2012, the Centre de Recherches Mathematiques was at the center of many interesting developments in geometric and spectral analysis, with a thematic program...
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SubjectTerms Congresses
Geometric analysis
Geometric analysis -- Congresses
Spectrum analysis
Spectrum analysis -- Congresses
TableOfContents A New Proof of a Bismut-Zhang Formula for Some Class of Representations -- Tunneling, the Quillen Metric and Analytic Torsion for High Powers of a Holomorphic Line Bundle -- Simple Spectrum and Rayleigh Quotients -- Smooth and Singular Kähler–Einstein Metrics -- Complex <inline-formula content-type="math/mathml"> b b </inline-formula>-Manifolds -- Iterative Structures on Singular Manifolds -- The Fundamental Gap and One-Dimensional Collapse -- The Logarithmic Singularities of the Green Functions of the Conformal Powers of the Laplacian -- A Symbolic Calculus for Fourier Integral Operators -- Strichartz Estimates on Exterior Polygonal Domains -- Probabilistic Sobolev Embeddings, Applications to Eigenfunctions Estimates -- Random Smooth Functions on Compact Riemannian Manifolds -- On the Exponential Decay of Laplacian Eigenfunctions in Planar Domains with Branches -- Bounds on the Principal Frequency of the <inline-formula content-type="math/mathml"> p p </inline-formula>-Laplacian
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 Laplacian -- 4. 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 -- 1. Introduction -- 2. Global Strichartz Estimates for the Model Problems -- 3. Local Smoothing Estimates for and on Euclidean Cones -- 4. Proof of Theorem 1 -- 5. A brief comment on nonlinear applications -- References -- Probabilistic Sobolev Embeddings, Applications to Eigenfunctions Estimates -- 1. Introduction -- 2. Probabilistic estimates -- 3. Eigenbases -- 4. Other manifolds -- 5. Probability calculus on spheres -- References -- Random Smooth Functions on Compact Riemannian Manifolds -- 1. The setup -- 2. The white noise limit of the variational complexity -- 3. Statistical reconstruction of the geometry of -- 4. A probabilistic interpretation of the Gauss-Bonnet theorem -- 5. Outline of proofs -- References -- On the Exponential Decay of Laplacian Eigenfunctions in Planar Domains with Branches -- 1. Introduction -- 2. Extension for Robin boundary condition -- 3. Illustrations -- References
Bounds on the Principal Frequency of the -Laplacian -- 1. Overview of the -Laplacian -- 2. Introduction and main results -- 3. Lower bounds involving the inradius in higher dimensions -- 4. Lower bounds involving eigenvalues of the -Laplace operator on manifolds -- 5. Proofs -- Acknowledgements -- References -- Back Cover
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 Kähler class -- Acknowledgments -- References -- Smooth and Singular Kähler-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 Monge-Ampère equations -- 8. The asymptotically logarithmic world -- 9. The logarithmic Calabi problem -- Acknowledgements -- 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 algebra -- 4. Shapiro-Lopatinskij edge-ellipticity -- 5. Iterated Mellin quantisation -- 6. Toeplitz edge problems -- References -- The Fundamental Gap and One-Dimensional Collapse -- 1. Motivation and results
Title Geometric and Spectral Analysis
URI https://www.ams.org/conm/630/
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