Recent progress in conformal geometry / Abbas Bahri, Yongzhong Xu.

Format:

Book

Author/Creator:

Bahri, Abbas.

Contributor:

Xu, Yongzhong.

Series:

Imperial College Press advanced texts in mathematics ; v. 1.

Imperial College Press advanced texts in mathematics ; vol. 1

Language:

English

Subjects (All):

Conformal geometry.

Physical Description:

1 online resource (522 p.)

Edition:

1st ed.

Place of Publication:

London : Imperial College Press, c2007.

Language Note:

English

Summary:

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 Legrend

Contents:

Preface A. Bahri and Y. Xu; Contents; 1. Sign-Changing Yamabe-Type Problems; 1.1 General Introduction; 1.2 Results and Conditions; 1.3 Conjecture 2 and Sketch of the Proof of Theorem 1; Outline; 1.4 The Difference of Topology; 1.5 Open Problems; 1.6 Preliminary Estimates and Expansions, the Principal Terms; 1.7 Preliminary Estimates; 1.8 Proof of the Morse Lemma at Infinity When the Concentrations are Comparable; 1.9 Redirecting the Estimates, Estimates on - ̄vi-H1; Bibliography; 2. Contact Form Geometry; 2.1 General Introduction

2.2 On the Dynamics of a Contact Structure along a Vector Field of its Kernel2.3 Appendix 1; 2.4 The Normal Form of (a, v) Near an Attractive Periodic Orbit of v; 2.5 Compactness; 2.6 Transmutations; 2.7 On the Morse Index of a Functional Arising in Contact Form Geometry; 2.8 Calculation of ?2J (x ).u2.u2; 2.9 Calculation of ?2J (x ).u2.u4; 2.10 Other Second Order Derivatives; 2.11Appendix; Bibliography

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 199, 509).

ISBN:

9786611120658

9781281120656

1281120650

9781860948602

186094860X

OCLC:

476099834