**Contemporary Mathematics**

Volume: 681;
2017;
184 pp;
Softcover

MSC: Primary 32;

**Print ISBN: 978-1-4704-2255-4
Product Code: CONM/681**

List Price: $111.00

AMS Member Price: $88.80

MAA Member Price: $99.90

**Electronic ISBN: 978-1-4704-3663-6
Product Code: CONM/681.E**

List Price: $111.00

AMS Member Price: $88.80

MAA Member Price: $99.90

# Analysis and Geometry in Several Complex Variables

Share this page *Edited by *
*Shiferaw Berhanu; Nordine Mir; Emil J. Straube*

This volume contains the proceedings of the
workshop on Analysis and Geometry in Several Complex Variables, held
from January 4–8, 2015, at Texas A&M University at Qatar, Doha,
Qatar.

This volume covers many topics of current interest in several complex
variables, CR geometry, and the related area of overdetermined
systems of complex vector fields, as well as emerging trends in these
areas.

Papers feature original research on diverse topics such as the
rigidity of CR mappings, normal forms in CR geometry, the d-bar
Neumann operator, asymptotic expansion of the Bergman kernel, and
hypoellipticity of complex vector fields. Also included are two
survey articles on complex Brunn-Minkowski theory and the regularity
of systems of complex vector fields and their associated Laplacians.

#### Readership

Graduate students and research mathematicians interested in various aspects of several complex variables.

# Table of Contents

## Analysis and Geometry in Several Complex Variables

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Real and complex Brunn-Minkowski theory 110
- 1. Introduction. 110
- 2. Convexity in \Rⁿ. 211
- 3. Beginning of discussion of the complex case. Basic notions and failure of naive analogies of Prekopa’s theorem. 716
- 4. First version of complex Prekopa. 1524
- 5. Interpretations of the complex Prekopa theorem I. 1827
- 6. Interpretation of the complex Prekopa theorem II. 2130
- 7. An application to the Ohsawa-Takegoshi extension theorem. 2433
- References 2635

- Properties of solutions of a class of hypocomplex vector fields 2938
- Analysis on the intersection of pseudoconvex domains 5160
- Distributional boundary values: some new perspectives 6574
- Infinitesimal and local rigidity of mappings of CR manifolds 7180
- On some systems of real or complex vector fields and their related Laplacians 8594
- 1. Introduction of some notations and definitions 8594
- 2. On the notion of maximal estimates 8897
- 3. Preliminary remarks and properties about (𝐿) and Δ_{𝐿} 91100
- 4. On systems of real vector fields and Hörmander’s operators 95104
- 5. The case of involutive systems 100109
- 6. On systems of complex vector fields satisfying “bracket conditions” 117126
- References 121130

- On the HJY Gap Conjecture in CR geometry vs. the SOS Conjecture for polynomials 125134
- Lower-dimensional Fefferman measures via the Bergman kernel 137146
- Normal forms in Cauchy-Riemann geometry 153162
- Bergman kernel asymptotics through perturbation 179188
- Back Cover Back Cover1194