Exponential Decay Estimates and Smoothness of the Moduli Space of Pseudoholomorphic Curves
Published on 30. September 2024
Book
Paperback/Softback
140 pages
978-1-4704-7106-4 (ISBN)
Description
The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
ISBN-13
978-1-4704-7106-4 (9781470471064)
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Schweitzer Classification
Persons
Kenji Fukaya, State University of New York, Stony Brook, New York, Yong-Geun Oh, Institute for Basic Sciences, Pohang, Korea, and POSTECH, Pohang, Korea, Hiroshi Ohta, Nagoya University, Japan, and Kaoru Ono, Kyoto University, Japan.
Content
1. Introduction
2. Preliminaries
3. Statement of the gluing theorem
4. Proof of the gluing theorem I: Cut-off functions and weighted Sobolev norm
5. Proof of the gluing theorem II: Gluing by alternating method
6. Exponential decay of $T$ derivatives
7. Surjectivity and injectivity of the gluing map
8. Exponential decay estimate implies smoothness of coordinate change
A. Error term estimate of non-linear Cauchy-Riemann equation I
B. Estimate of Parallel transport 1
C. Error term estimate of non-linear Cauchy-Riemann equation II
D. Estimate of Parallel transport 2
E. Estimate of the non-linearity of Exponential map
F. Estimate of Parallel transport 3
G. Estimate of $T$ derivative of the error term of non-linear Cauchy-Riemann equation
H. Proof of Lemma
2. Preliminaries
3. Statement of the gluing theorem
4. Proof of the gluing theorem I: Cut-off functions and weighted Sobolev norm
5. Proof of the gluing theorem II: Gluing by alternating method
6. Exponential decay of $T$ derivatives
7. Surjectivity and injectivity of the gluing map
8. Exponential decay estimate implies smoothness of coordinate change
A. Error term estimate of non-linear Cauchy-Riemann equation I
B. Estimate of Parallel transport 1
C. Error term estimate of non-linear Cauchy-Riemann equation II
D. Estimate of Parallel transport 2
E. Estimate of the non-linearity of Exponential map
F. Estimate of Parallel transport 3
G. Estimate of $T$ derivative of the error term of non-linear Cauchy-Riemann equation
H. Proof of Lemma