Download Gromov’s Compactness Theorem for Pseudo-holomorphic Curves by Christoph Hummel PDF

By Christoph Hummel

Mikhail Gromov brought pseudo-holomorphic curves into symplectic geometry in 1985. because then, pseudo-holomorphic curves have taken on nice significance in lots of fields. the purpose of this ebook is to provide the unique evidence of Gromov's compactness theorem for pseudo-holomorphic curves intimately. neighborhood homes of pseudo-holomorphic curves are investigated and proved from a geometrical perspective. houses of specific curiosity are isoperimetric inequalities, a monotonicity formulation, gradient bounds and the elimination of singularities. a different bankruptcy is dedicated to suitable beneficial properties of hyperbolic surfaces, the place pairs of pants decomposition and thickthin decomposition are defined. The publication is basically self-contained and may even be obtainable to scholars with a simple wisdom of differentiable manifolds and masking areas.

Show description

Read Online or Download Gromov’s Compactness Theorem for Pseudo-holomorphic Curves PDF

Similar geometry books

Geometria Analitica: Una introduccion a la geometria

Este texto constituye una introducción al estudio de este tipo de geometría e incluye ilustraciones, ejemplos, ejercicios y preguntas que permiten al lector poner en práctica los conocimientos adquiridos.

Foliations in Cauchy-Riemann Geometry (Mathematical Surveys and Monographs)

The authors research the connection among foliation thought and differential geometry and research on Cauchy-Riemann (CR) manifolds. the most items of research are transversally and tangentially CR foliations, Levi foliations of CR manifolds, recommendations of the Yang-Mills equations, tangentially Monge-AmpГѓВ©re foliations, the transverse Beltrami equations, and CR orbifolds.

Vorlesungen über höhere Geometrie

VI zahlreiche Eigenschaften der Cayley/Klein-Raume bereitgestellt. AbschlieBend erfolgt im Rahmen der projektiven Standardmodelle eine Einflihrung in die Kurven- und Hyperflachentheorie der Cay ley/Klein-Raume (Kap. 21,22) und ein kurzgefaBtes Kapitel liber die differentialgeometrische Literatur mit einem Abschnitt liber Anwendungen der Cayley/Klein-Raume (Kap.

Kinematic Geometry of Gearing, Second Edition

Content material: bankruptcy 1 creation to the Kinematics of Gearing (pages 3–52): bankruptcy 2 Kinematic Geometry of Planar apparatus the teeth Profiles (pages 55–84): bankruptcy three Generalized Reference Coordinates for Spatial Gearing—the Cylindroidal Coordinates (pages 85–125): bankruptcy four Differential Geometry (pages 127–159): bankruptcy five research of Toothed our bodies for movement iteration (pages 161–206): bankruptcy 6 The Manufacture of Toothed our bodies (pages 207–248): bankruptcy 7 Vibrations and Dynamic quite a bit in equipment Pairs (pages 249–271): bankruptcy eight apparatus layout score (pages 275–326): bankruptcy nine The built-in CAD–CAM technique (pages 327–361): bankruptcy 10 Case Illustrations of the built-in CAD–CAM method (pages 363–388):

Additional info for Gromov’s Compactness Theorem for Pseudo-holomorphic Curves

Sample text

D Chapter IV Hyperbolic surfaces This chapter describes the pairs of pants decomposition and the thick-thin decomposition of oriented complete hyperbolic surfaces of finite area. Using the pairs of pants decomposition, one gets, roughly speaking, a parametrization of the space of hyperbolic structures on such a surface which coincides with the space of its complex structures. The thick-thin decomposition gives a classification of the thin parts of a hyperbolic surface, which are the components of small injectivity radius.

Area minimizing maps from a compact surface with boundary to some Euclidean space satisfy the well-known isoperimetric inequality 4n . area ~ (length of boundary)2 (see Appendix A) which is "similar" to the one claimed in the lemma. II. 1. Let R = injrad(M, Il) be the injectivity radius of M. 1). Let expp := expp IBR(O) denote the exponential map of Mat p restricted to the R-ball BR(O) c (TpM,Jp,ll p ) where p is an arbitrary point in M fixed from now on. We identify canonically the tangent spaces to TpM with TpM itself.

2. Chapter III Higher order derivatives This chapter is concerned with the estimate of higher order derivatives of f-holomorphic maps. For that purpose the differentials of f -holomorphic maps are made into pseudo-holomorphic maps to which the Gromov-Schwarz lemma applies. This is used in the proof of Gromov's theorem on the removal of singularities for f-holomorphic maps. It is a generalization of a theorem of Riemann from complex analysis, which says that a holomorphic map f: S \ {a} ~ S2 from a Riemann surface minus an interior point a to the Riemann sphere can be extended to a holomorphic map S ~ S2, provided f does not have an essential singularity at a.

Download PDF sample

Rated 4.80 of 5 – based on 9 votes