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.
Gromov's Compactness Theorem for Pseude-holomorphic Curves
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"...the book provides a self-contained and for the most part excellent elaboration of Gromov's proof of the compactness theorem."
-- Mathematical Reviews
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Inside This Book
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First Sentence:
We need only some elementary properties of Riemannian manifolds which we summarize here. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
degenerate boundary components, squeezing theorem, monotonicity lemma, standard cusp, simple closed geodesics, classical isoperimetric inequality, injectivity radius, hyperbolic surface, geodesic segment, symplectic topology, free homotopy class, compactness theorem, cusp curve, holomorphic curves, quantum cohomology, symplectic manifolds, hyperbolic structures, simple closed loops, symplectic structure, symplectic geometry, universal covering space, homology class, complex manifold, isoperimetric inequalities Key Phrases - Capitalized Phrases (CAPs): (learn more)
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We need only some elementary properties of Riemannian manifolds which we summarize here. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
degenerate boundary components, squeezing theorem, monotonicity lemma, standard cusp, simple closed geodesics, classical isoperimetric inequality, injectivity radius, hyperbolic surface, geodesic segment, symplectic topology, free homotopy class, compactness theorem, cusp curve, holomorphic curves, quantum cohomology, symplectic manifolds, hyperbolic structures, simple closed loops, symplectic structure, symplectic geometry, universal covering space, homology class, complex manifold, isoperimetric inequalities Key Phrases - Capitalized Phrases (CAPs): (learn more)
Applying Lemma New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 34
books:
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- Riemannian Geometry (Universitext) by Sylvestre Gallot in Back Matter (1), Back Matter (2), and Back Matter (3)
- Floer Memorial Volume (Progress in Mathematics) by Helmut Hofer in Back Matter (1), and Back Matter (2)
- Symplectic Invariants and Hamiltonian Dynamics (Birkhauser Advanced Texts) by Helmut Hofer in Back Matter (1), and Back Matter (2)
- Geometric Inequalities (Grundlehren Der Mathematischen Wissenschaften) by Yu. D. Burago in Back Matter
- Riemannian Geometry and Geometric Analysis (Universitext) by Jürgen Jost in Back Matter
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