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Full 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.
Contents
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
