Recent Progress In Conformal Geometry
Seiten
2007
Imperial College Press (Verlag)
978-1-86094-772-8 (ISBN)
Imperial College Press (Verlag)
978-1-86094-772-8 (ISBN)
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New ground is broken with the establishment of a Morse lemma at infinity for sign-changing Yamabe-type problems. This book presents a front of research in conformal geometry, on sign-changing Yamabe-type problems and contact form geometry in particular.
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.
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.
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.
| Reihe/Serie | Icp Advanced Texts In Mathematics ; 1 |
|---|---|
| Verlagsort | London |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-86094-772-7 / 1860947727 |
| ISBN-13 | 978-1-86094-772-8 / 9781860947728 |
| Zustand | Neuware |
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