Gromov's Compactness Theorem for Pseudo-Holomorphic Curves

By: Christoph Hummel

Write A Review

Hardcover | 1 December 1996

At a Glance

Hardcover
148 Pages

Dimensions(cm)
23.39 x 15.6 x 0.97

Hardcover

$101.07

or 4 interest-free payments of $25.27 with

or

Aims to ship in 7 to 10 business days

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.

Industry Reviews

"...the book provides a self-contained and for the most part excellent elaboration of Gromov's proof of the compactness theorem."
-- Mathematical Reviews

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Geometry

The Golden Ratio

Divine Beauty of Mathematics

Hardcover

RRP $55.00

$43.90

20%
OFF

Concise Complex Analysis (Revised Edition)

Hardcover

RRP $178.99

$170.25

$2ND STEP MATH OLYMPIAD PROB(V7) : Mathematical Olympiad - DEREK HOLTON$

2ND STEP MATH OLYMPIAD PROB(V7)

Mathematical Olympiad

Paperback

RRP $68.99

$43.95

36%
OFF

Geometry, Perspect Drawing, & Mechanisms

Hardcover

RRP $147.99

$140.75

MODERN DIFF GEOMETRY FOR PHYS (2ED)(V61)

Second Edition

Paperback

RRP $77.99

$74.25

BLACK FRIDAY

Clouds Are Not Spheres

A Portrait of Benoit Mandelbrot, the Founding Father of Fractal Geometry

Hardcover

RRP $104.99

$26.25

75%
OFF

BLACK FRIDAY

BIRTH OF CHINA SEEN THROUGH POETRY, THE

Paperback

RRP $39.99

$9.95

75%
OFF

Nankai Symposium on Mathematical Dialogues : Celebrating the 110th anniversary of the birth of Prof. S.-S. Chern - Yang-Hui He

$76.75

28%
OFF

A Stitch in Line : Mathematics and One-Stitch Sashiko - Katherine Seaton

$39.25

Regents Exams and Answers : Geometry, Sixth Edition - Barron's Educational Series

$28.25

50%
OFF

Introduction	p. 1
Preliminaries
Riemannian manifolds	p. 5
Almost complex and symplectic manifolds	p. 7
J-holomorphic maps	p. 10
Riemann surfaces and hyperbolic geometry	p. 11
Annuli	p. 17
Estimates for area and first derivatives
Gromov's Schwarz- and monotonicity lemma	p. 21
Area of J-holomorphic maps	p. 22
Isoperimetric inequalities for J-holomorphic maps	p. 23
Proof of the Gromov-Schwarz lemma	p. 30
Higher order derivatives
I-jets of J-holomorphic maps	p. 35
Removal of singularities	p. 41
Converging sequences of J-holomorphic maps	p. 45
Variable almost complex structures	p. 46
Hyperbolic surfaces
Hexagons	p. 49
Building hyperbolic surfaces from pairs of pants	p. 55
Pairs of pants decomposition	p. 59
Thick-thin decomposition	p. 68
Compactness properties of hyperbolic structures	p. 70
The compactness theorem
Cusp curves	p. 79
Proof of the compactness theorem	p. 82
Bubbles	p. 91
The squeezing theorem
Discussion of the statement	p. 99
Proof modulo existence result for pseudo-holomorphic curves	p. 102
The analytical setup: A rough outline	p. 104
The required existence result	p. 110
The classical isoperimetric inequality	p. 115
The C[superscript k]-topology	p. 117
References on pseudo-holomorphic curves	p. 121
Bibliography	p. 125
Index	p. 129
Table of Contents provided by Blackwell. All Rights Reserved.

Gromov's Compactness Theorem for Pseudo-Holomorphic Curves

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Geometry

The Golden Ratio

Divine Beauty of Mathematics

Concise Complex Analysis (Revised Edition)

2ND STEP MATH OLYMPIAD PROB(V7)

Mathematical Olympiad

Geometry, Perspect Drawing, & Mechanisms

MODERN DIFF GEOMETRY FOR PHYS (2ED)(V61)

Second Edition

Clouds Are Not Spheres

A Portrait of Benoit Mandelbrot, the Founding Father of Fractal Geometry

BIRTH OF CHINA SEEN THROUGH POETRY, THE

Nankai Symposium on Mathematical Dialogues

Celebrating the 110th anniversary of the birth of Prof. S.-S. Chern

Perspectives on Four Decades of Algebraic Geometry, Volume 1

In Memory of Alberto Collino

Perspectives on Four Decades of Algebraic Geometry, Volume 2

In Memory of Alberto Collino

Advances in Algebra Analysis and Topology

The Four Corners of Mathematics

A Brief History, from Pythagoras to Perelman

A Stitch in Line

Mathematics and One-Stitch Sashiko

Women in Mathart

Research, Creativity, and Teaching

Mathematical Analysis

Theory and Applications

The Four Corners of Mathematics

A Brief History, from Pythagoras to Perelman

A Stitch in Line

Mathematics and One-Stitch Sashiko

Let's Review Regents

Geometry, Sixth Edition

Regents Exams and Answers

Geometry, Sixth Edition

Numerical Geometry, Grid Generation and Scientific Computing

Proceedings of the 11th International Conference, NUMGRID 2022

Make - Trigonometry

Build your way from triangles to analytic geometry

Lectures on Khler Groups

Princeton Mathematical Series

An Introduction to Module Theory

Oxford Graduate Texts in Mathematics

An Introduction to Module Theory

Oxford Graduate Texts in Mathematics

This product is categorised by

Popular Searches