Recent Progress In Conformal Geometry
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€202.12
A01=Abbas Bahri
A01=Yongzhong Xu
Author_Abbas Bahri
Author_Yongzhong Xu
Category=PBMP
Category=PBMS
Contact Form Geometry
Critical Point at Infinity
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Legendrian Curves
Variational Problems
Yamabe-Type Problems
Product details
- ISBN 9781860947728
- Publication Date: 09 Apr 2007
- Publisher: Imperial College Press
- Publication City/Country: GB
- Product Form: Hardback
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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.
