Recent progress in conformal geometry

Author(s)

• Bahri, A.
• Xu, Yongzhong

Bibliographic Information

Recent progress in conformal geometry

Abbas Bahri, Yongzhong Xu

（ICP advanced texts in mathematics / series editor, Dennis Barden, v. 1）

Imperial College Press , Distributed by World Scientific, c2007

Note

Includes bibliographical references (p. 509)

Description and Table of Contents

Description

This book presents a new front of research in conformal geometry, on sign-changing Yamabe-type problems and contact form geometry in particular. New ground is broken with the establishment of a Morse lemma at infinity for sign-changing Yamabe-type problems. This family of problems, thought to be out of reach a few years ago, becomes a family of problems which can be studied: the book lays the foundation for a program of research in this direction.In contact form geometry, a cousin of symplectic geometry, the authors prove a fundamental result of compactness in a variational problem on Legrendrian curves, which allows one to define a homology associated to a contact structure and a vector field of its kernel on a three-dimensional manifold. The homology is invariant under deformation of the contact form, and can be read on a sub-Morse complex of the Morse complex of the variational problem built with the periodic orbits of the Reeb vector-field. This book introduces, therefore, a practical tool in the field, and this homology becomes computable.

Table of Contents

• Sign-Changing Yamabe-Type Problems: General Introduction
• Results and Conditions
• Conjecture 2 and Sketch of the Proof of Theorem 1
• Outline
• The Difference of Topology
• Open Problems
• Preliminary Estimates and Expansions, the Principal Terms
• Preliminary Estimates
• Proof of the Morse Lemma at Infinity when the Concentrations are Comparable
• Proof of the Morse Lemma at Infinity
• Contact Form Geometry: General Introduction
• On the Dynamics of a Contact Structure Along a Vector Field of Its Kernel
• Appendix 1
• The Normal Form of ( , ) Near an Attractive Periodic Orbit of
• Compactness
• Transmutations
• On the Morse Index of a Functional Arising in Contact Form Geometry
• and other chapters.

by "Nielsen BookData"

Details

• NCID: BA81854935
• ISBN:
  • 9781860947728
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: London,Hackensack, NJ
• Pages/Volumes: xii, 509 p.
• Size: 24 cm
• Subject Headings:
  • LCSH : Conformal geometry
• Parent Bibliography ID:
  • BA81854480