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.
1. Introduction
2. Some preparations
3. Bi-Lipschitz equivalence
4. Proof of Theorem
5. Proof of Theorem
6. Quantifying the optimality of the optimal bi-Lipschitz constants
7. The core argument
Jian Ding, Peking University, Beijing, People's Republic of China, Zherui Fan, Peking University, Beijing, People's Republic of China, and Lu-Jing Huang, Fujian Normal University, Fuzhou, People's Republic of China
