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Book synopsis

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.

Book details

Book category Books in English Mathematics & science Mathematics Geometry

• Full title: Recent Progress In Conformal Geometry
• Author: Abbas Bahri, Yongzhong Xu
• Language: English
• Binding: Hardback
• Number of pages: 524
• EAN: 9781860947728
• ISBN: 1860947727
• ID: 05121908
• Publisher: Imperial College Press
• Weight: 854 g
• Dimensions: 231 × 161 × 33 mm
• Date of publishing: 09. April 2007

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