Selected papers of Masatake Kuranishi

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Selected papers of Masatake Kuranishi

editor-in-chief, Heisuke Hironaka ; editors, Takao Akahori ... [et al.]

World Scientific, c2013

Available at  / 22 libraries

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Other editors: Gen Komatsu, Kimio Miyajima, Makoto Namba, Duong H. Phong, Keizo Yamaguchi

Includes bibliographical references

Description and Table of Contents

Description

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.

Table of 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 F E Erman'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 Szego Kernel: I
  • An Approach to the Cartan Geometry II: CR Manifolds
  • The Formula for the Singularity of Szego Kernel: II
  • and other papers.

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