Recent progress in conformal geometry

書誌事項

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

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注記

Includes bibliographical references (p. 509)

内容説明・目次

内容説明

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.

目次

  • 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.

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詳細情報
  • NII書誌ID(NCID)
    BA81854935
  • ISBN
    • 9781860947728
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    London,Hackensack, NJ
  • ページ数/冊数
    xii, 509 p.
  • 大きさ
    24 cm
  • 件名
  • 親書誌ID
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