Last edited by Tojaran
Sunday, July 26, 2020 | History

3 edition of Gromov"s compactness theorem for pseudo-holomorphic curves found in the catalog.

Gromov"s compactness theorem for pseudo-holomorphic curves

by Christoph Hummel

  • 268 Want to read
  • 24 Currently reading

Published by Birkhäuser Verlag in Basel, Boston .
Written in English

    Subjects:
  • Riemann surfaces.,
  • Holomorphic mappings.

  • Edition Notes

    Includes bibliographical references (p. [125]-127) and index.

    StatementChristoph Hummel.
    SeriesProgress in mathematics ;, v. 151, Progress in mathematics (Boston, Mass.) ;, v. 151.
    Classifications
    LC ClassificationsQA333 .H85 1997
    The Physical Object
    Paginationviii, 131 p. :
    Number of Pages131
    ID Numbers
    Open LibraryOL666307M
    ISBN 103764357355, 0817657355
    LC Control Number97011972

    This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including positivity of intersections, and applications to Lagrangian embeddings problems. The Compactness Theorem states: F is satisfiable ⟺ every finite subset of F is satisfiable.

    Bibliographie.- 3: Pseudo-holomorphic curves and applications.- V Some properties of holomorphic curves in almost complex manifolds.- 1 The equation $$ \bar \partial f$$ in C.- 2 Regularity of holomorphic curves.- 3 Other local properties.- 4 Properties of the area of holomorphic curves.- 5 Gromov's compactness theorem for holomorphic curves One novel aspect of this treatment is the uniform treatment of both closed and open cases and a complete proof of the boundary regularity theorem of weak solutions of pseudo-holomorphic curves with totally real boundary conditions. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory.

    The compactness theorem, in the forms of Theorems and , is due to Gödel; in fact, as explained in the beginning of Section [Henkin's Method], the theorem was for Gödel a simple corollary (we could even say an unexpected corollary, a rather strange remark!) of his "completeness theorem" of logic, in which he showed that a finite. We give a proof of the Gromov compactness theorem using the language of stable curves (i.e. cusp-curve of Gromov, or stable maps of Kontsevich and Manin) in general setting: An almost complex structure on a target manifold is only continuous and can vary; the curves are only assumed to have fixed ``topological type'', in particular they can be non-closed and the complex structures on them can.


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Gromov"s compactness theorem for pseudo-holomorphic curves by Christoph Hummel Download PDF EPUB FB2

Gromov's Compactness Theorem for Pseudo-Holomorphic Curves (Progress in Mathematics) Softcover reprint of the original 1st ed. Edition. Find all the books, read about the author, and by: Mikhail Gromov introduced pseudo-holomorphic curves into symplectic geometry in 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 Brand: Birkhäuser Basel. This book presents 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.

Mikhail Gromov introduced pseudo-holomorphic curves into symplectic geometry in This book aims to present in detail the original proof for Gromov's compactness theorum for pseudo-holomorphic curves. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint.

Properties of particular interest are isoperimetric inequalities, a. The main goal of this master thesis is to give a self-contained proof of the Gromov compactness theorem for pseudoholomorphic curves and the non-squeezing theorem in symplectic topology. Pseudoholomorphic curves are smooth maps from a Riemann surface into an almost complex manifold that respect the almost complex structures.

Abstract. We give a complete proof for Gromov's compactness theorem for pseudo holomorphic curves both in the case of closed curves and curves with boundary. Introduction In M. Gromov invented the beautiful theory of pseudo holomorphic curves and made it a powerful tool in symplectic geometry [Gro].

On a sym. Part of the Progress in Mathematics book series (PM, volume ) Abstract In this chapter we formulate the compactness theorem for J -holomorphic curves and present Gromov’s proof in detail. There's a proof of compactness using Skolem functions in the book "Elements of Mathematical Logic.

Model Theory" by Kreisel and Krivine. (I'm assuming here that the English version matches the French, because the latter is the one I checked.) It presupposes the compactness theorem. For Gromov's compactness theorem in Riemannian geometry, see that article.

In the mathematical field of symplectic topology, Gromov's compactness theorem states that a sequence of pseudoholomorphic curves in an almost complex manifold with a uniform energy bound must have a subsequence which limits to a pseudoholomorphic curve which may have nodes or (a finite tree of).

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. Presentation: Gromov Compactness Theorem Keywords: almost complex structure, hermitian metric, symplectic form, area, cusp curves, weak convergence.

We will discuss the concepts and ideas about Gromov compactness theorem in this presentation. For example, the closed-surface version of GCT is Theorem 1 (GCT).

Compactness for punctured holomorphic curves Cieliebak, K. and Mohnke, K., Journal of Symplectic Geometry, ; An algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves Pardon, John, Geometry & Topology, ; A sharp compactness theorem for genus-one pseudo-holomorphic maps Zinger, Aleksey, Geometry & Topology, Gromov showed that certain moduli spaces of pseudoholomorphic curves (satisfying additional specified conditions) are compact, and described the way in which pseudoholomorphic curves can degenerate when only finite energy is assumed.

DOI: /CAGv8.n1.a4 Corpus ID: Pseudo-holomorphic Curves and the Weinstein Conjecture @inproceedings{ChenPseudoholomorphicCA, title={Pseudo-holomorphic Curves and the Weinstein Conjecture}, author={Weimin Chen}, year={} }. So the areas of pseudoholomorphic curves, in this situation, are controlled by straightfor- ward topological data.

This allowed Gromov to prove a partial compactness theorem for the moduli spaces. For example, consider as before the maps from the Riemann sphere to the complex projective plane.

It seems to me that a hypothesis is missing - i.e. a "uniform control" on the diameters of every set in $\mathcal{C}$. This is the second textbook in which I've found this (wrong?) version of the theorem (in the Gromov's original paper, for example, Gromov uses the uniform compactness).

Am I. singular set uniform gradient bounds along the boundary curve of the holomorphic discs can be obtained by geometric arguments.

In order to unify the argumentation and for a deeper understanding of the Reeb dynamics on a contactmanifold Gromov convergence of holomorphic discs is required for totally real boundary conditions. Date: Another section treats the compactness theorem for pseudo-holomorphic curves. A special feature of the presented proof is that it works for sequences of almost complex structures only converging in the C0-topology.

This is essential in the application to the symplectic isotopy problem. Download PDF: Sorry, we are unable to provide the full text but you may find it at the following location(s): (external link).

Bibliographie.- 3: Pseudo-holomorphic curves and applications.- V Some properties of holomorphic curves in almost complex manifolds.- 1 The equation $$ \bar \partial f$$ in C.- 2 Regularity of holomorphic curves.- 3 Other local properties.- 4 Properties of the area of holomorphic curves.- 5 Gromov's compactness theorem for holomorphic curves.

In mathematical logic, the compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important tool in model theory, as it provides a useful method for constructing models of any set of sentences that is finitely consistent.

The compactness theorem for the propositional calculus is a consequence of.Gromov compactness theorem for stable curves.In Pure and Applied Mathematics, D Weighted norms and the Kondrachov compactness theorems tor unbounded domains.

The Kondrachov compactness theorem () fails for general unbounded domains (e.g., ℝ N), and as mentioned in the text, this loss of compactness is crucial for many interesting nonlinearit is interesting to note that the Kondrachov compactness theorem .