9781461265764 - Flow Lines and Algebraic Invariants in Contact Form Geometry (Progress in Nonlinear Differential Equations and Their Applications, Band 53) von Bahri, Abbas (2 Ergebnisse)

Zustand: New. In.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - This text features a carefultreatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology). In particular, this work develops a novel algebraic tool in this field: rooted in the concept of critical points at infinity, the new algebraic invariants defined here are useful in the investigation of contact structures and Reeb vector fields.The book opens with a review of prior results and then proceeds through an examination of variational problems, non-Fredholm behavior, true and false critical points at infinity, and topological implications. An increasing convergence with regular and singular Yamabe-type problems is discussed, andthe intersectionbetweencontact form and Riemannian geometryis emphasized, with a specific focus on a unified approach to non-compactness in both disciplines. Fully detailed, explicit proofs and a number of suggestions for further research are provided throughout.Rich in open problems and written with a global view of several branches of mathematics, this textlays thefoundationfor new avenues of studyin contact form geometry.Graduate students and researchers in geometry,partial differential equations, and related fields will benefit from the book's breadth and unique perspective.