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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| Hlavní autoři: | , , , , , |
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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
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Providence, Rhode Island
American Mathematical Society
03.12.2014
Centre de Recherches Mathematiques Centre de Recherches Mathématiques |
| Vydání: | 1 |
| Edice: | Contemporary Mathematics |
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| ISBN: | 9781470410438, 1470410435 |
| ISSN: | 0271-4132, 1098-3627 |
| On-line přístup: | Získat plný text |
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- 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