Selected Papers of Masatake Kuranishi

https://doi.org/10.1142/8801 | June 2013

Pages: 656

Editor-in-chief:
Heisuke Hironaka (Japan Association for Mathematical Sciences, Japan)

Edited by:
Takao Akahori (University of Hyogo Prefecture, Japan),
Gen Komatsu (Osaka University, Japan),
Kimio Miyajima (Kagoshima University, Japan),
Makoto Namba (Otemon Gakuin University, Japan),
Duong H Phong (Columbia University, USA), and
Keizo Yamaguchi (Hokkaido University, Japan)

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ISBN: 978-981-4508-13-1 (hardcover) USD 240.00 Add to cart

This book is a selection of Masatake Kuranishi's papers. Born in 1924, Kuranishi produced deep and far-reaching results in geometry over his career. Of his voluminous contributions, this book focuses on his later works: (i) his work on locally complete families of deformation of compact complex manifolds. Kuranishi was first to prove the fundamental results of the existence of complete families whose parameter spaces are today called Kuranishi spaces. His result is highly influential in deformation theory of various geometric objects. (ii) His work on the local embedding problem of Cauchy–Riemann structures. Kuranishi proved a fundamental embedding theorem in Cauchy–Riemann geometry. (iii) His work on Cartan Geometry and Szegö kernels. Mainly for his works on (i) and (ii), Kuranishi was awarded the Bergman Prize in 2000. Today, he is a professor emeritus of Columbia University.

Contents:

On Euclidean Local Groups Satisfying Certain Conditions
On Conditions of Differentiability of Locally Compact Groups
On E Cartan's Prolongation Theorem of Exterior Differential Systems
On the Local Theory of Continuous Infinite Pseudo Groups I
On the Local Theory of Continuous Infinite Pseudo Groups II
On the Locally Complete Families of Complex Analytic Structures
New Proof for the Existence of Locally Complete Families of Complex Structures
Strongly Pseudoconvex CR Structures over Small Balls: Part I, An a priori Estimate
Strongly Pseudoconvex CR Structures over Small Balls: Part II, A Regularity Theorem
Strongly Pseudoconvex CR Structures over Small Balls: Part III, An Embedding Theorem
Cartan Connections and CR Structures with Nondegenerate Levi-Form
The Frame Bundles of CR Structures and the Bergman Kernel (I)
The Frame Bundles of CR Structures and the Bergman Kernel (II)
CR Geometry and Cartan Geometry
CR Structures and Fefferman's Conformal Structures
On a priori Estimate on a Manifold with Singularity on the Boundary
An Approach to the Cartan Geometry I: Conformal Riemann Manifolds
The Formula for the Singularity of Szegö Kernel: I
An Approach to the Cartan Geometry II: CR Manifolds
The Formula for the Singularity of Szegö Kernel: II