Gromov’s Compactness Theorem for Pseudo-holomorphic Curves

von Christoph Hummel

135 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

Mikhail Gromov introduced pseudo-holomorphic curves into symplectic geometry in 1985. Since then, pseudo-holomorphic curves have taken on great importance in many fields. The aim of this book is to present the original proof of Gromov's compactness theorem for pseudo-holomorphic curves in detail. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint. Properties of particular interest are isoperimetric inequalities, a monotonicity formula, gradient bounds and the removal of singularities. A special chapter is devoted to relevant features of hyperbolic surfaces, where pairs of pants decomposition and thickthin decomposition are described. The book is essentially self-contained and should also be accessible to students with a basic knowledge of differentiable manifolds and covering spaces.

• Reihe: Progress in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Geometrie
• ISBN: 9783034898423
• Sprache: Englisch
• Erscheinungsdatum: 15.10.2012
• Größe: 23.5 x 15.5 cm
• Verlag: Springer Basel