Flow Lines and Algebraic Invariants in Contact Form Geometry

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, and the intersection between contact form and Riemannian geometry is 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 text lays the foundation for new avenues of study in 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.