Geometric and spectral analysis /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Albin, Pierre, 1976- (Editor ), Jakobson, Dmitry, 1970- (Editor ), Rochon, Frédéric, 1978- (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island ; Montréal, Québec : American Mathematical Society : Centre de Recherches Mathematiques, 2014.
Colección:Contemporary mathematics (American Mathematical Society). Centre de recherches mathématiques proceedings ; 613.
Temas:
Spectrum analysis > Congresses.
Geometric analysis > Congresses.
Analyse géométrique > Congrès.
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.
Conference papers and proceedings
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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

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