Recent progress in conformal geometry
Author(s)
Bibliographic Information
Recent progress in conformal geometry
（ICP advanced texts in mathematics / series editor, Dennis Barden, v. 1）
Imperial College Press , Distributed by World Scientific, c2007
Available at / 22 libraries
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
BAH||4||5200001577715
-
No Libraries matched.
- Remove all filters.
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"
