From Stein to Weinstein and Back: Symplectic Geometry of Affine Complex Manifolds (Colloquium Publications)

Cieliebak (Ludwig Maximilians U., Germany) and Eliashberg (Stanford U., US) add refinements to the existence theorem for Stein structures and present new results concerning surrounding of subsets by J-convex hypersurfaces. The opening chapters explore the basic properties of J-convex functions and hypersurfaces, construct special hypersurfaces needed for extending J-convex functions over handles, and review several h-principles. Later chapters develop a Morse-Smale type theory for J-convex functions and introduce Weinstein manifolds and their deformations. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)

This book is a remarkable mix of classical topics and research done by the authors over the last twenty years. It is both a textbook and a research monograph. ... [M]ore classical material...is presented from the perspective of their applications in the book. It is fascinating and refreshing to see these classical tools in action, combined and applied to create something new. The exposition is very beautiful; whenever possible, the geometry of the situation is fully brought out, and formulas and computations are used only to check a geometric intuition. --dmv

A beautiful and comprehensive introduction to this important field. --Dusa McDuff, Barnard College, Columbia University

This excellent book gives a detailed, clear, and wonderfully written treatment of the interplay between the world of Stein manifolds and the more topological and flexible world of Weinstein manifolds. Devoted to this subject with a long history, the book serves as a superb introduction to this area and also contains the authors' new results. --Tomasz Mrowka, MIT