**Contemporary Mathematics**

Volume: 630;
2014;
366 pp;
Softcover

MSC: Primary 58; 53; 60; 49; 46; 35;

Print ISBN: 978-1-4704-1043-8

Product Code: CONM/630

List Price: $126.00

AMS Member Price: $100.80

MAA Member Price: $113.40

**Electronic ISBN: 978-1-4704-2059-8
Product Code: CONM/630.E**

List Price: $126.00

AMS Member Price: $100.80

MAA Member Price: $113.40

# Geometric and Spectral Analysis

Share this page *Edited by *
*Pierre Albin; Dmitry Jakobson; Frédéric Rochon*

A co-publication of the AMS and Centre de Recherches Mathématiques

In 2012, the Centre de Recherches
Mathématiques 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, Kähler-Einstein metrics, analytic torsion,
and Strichartz estimates.

#### Readership

Graduate students and research mathematicians interested in geometric analysis and spectral geometry.

# Table of Contents

## Geometric and Spectral Analysis

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- A New Proof of a Bismut-Zhang Formula for Some Class of Representations 112 free
- 1. Introduction 112
- 2. The idea of the proof 213
- 3. The Milnor metric and the Farber-Turaev torsion 415
- 4. The Ray-Singer norm of the Refined Analytic Torsion 718
- 5. The Determinant Line Bundle over the Space of Representations 920
- 6. The Bismut-Zhang theorem for some non-unitary representations 1021
- References 1223

- Tunneling, the Quillen Metric and Analytic Torsion for High Powers of a Holomorphic Line Bundle 1526
- Simple Spectrum and Rayleigh Quotients 3344
- Smooth and Singular Kähler–Einstein Metrics 4556
- 1. Introduction 4556
- 2. The \KE equation 4758
- 3. \K edge geometry 4960
- 4. Existence and non-existence 6778
- 5. Energy functionals 8091
- 6. The Ricci continuity method 92103
- 7. A priori estimates for Monge–Ampère equations 99110
- 8. The asymptotically logarithmic world 112123
- 9. The logarithmic Calabi problem 124135
- Acknowledgements 127138
- References 127138

- Complex 𝑏-Manifolds 139150
- 1. Introduction 139150
- 2. Complex 𝑏-structures 140151
- 3. Holomorphic vector bundles 143154
- 4. The boundary of a complex 𝑏-manifold 145156
- 5. Local invariants 150161
- 6. Indicial complexes 153164
- 7. Underlying CR complexes 159170
- 8. Spectrum 163174
- 9. Indicial cohomology 165176
- Appendix A. Totally characteristic differential operators 170181
- References 171182

- Iterative Structures on Singular Manifolds 173184
- The Fundamental Gap and One-Dimensional Collapse 223234
- The Logarithmic Singularities of the Green Functions of the Conformal Powers of the Laplacian 247258
- Introduction 247258
- 1. The Heat Kernel of the Laplace Operator 249260
- 2. The Bergman Kernel of a Strictly Pseudoconvex Domain 252263
- 3. Ambient Metric and Conformal Powers of the Laplacian 255266
- 4. Local Conformal Invariants 257268
- 5. Scattering Theory and Conformal Fractional Powers of the Laplacian 259270
- 6. Green Functions of Elliptic Operators 263274
- 7. Green Functions and Conformal Geometry 265276
- 8. Proof of Theorem 7.3 268279
- References 270281

- A Symbolic Calculus for Fourier Integral Operators 275286
- Strichartz Estimates on Exterior Polygonal Domains 291302
- Probabilistic Sobolev Embeddings, Applications to Eigenfunctions Estimates 307318
- Random Smooth Functions on Compact Riemannian Manifolds 319330
- On the Exponential Decay of Laplacian Eigenfunctions in Planar Domains with Branches 337348
- Bounds on the Principal Frequency of the 𝑝-Laplacian 349360
- Back Cover Back Cover1378