Harmonic maps into singular spaces and Euclidean buildings.

• Other Authors: Lam, Kwan Hang.
• Format: Others
• Language: English; Chinese
• Published: 2001
• Subjects: Harmonic maps; Generalized spaces
• Online Access: http://library.cuhk.edu.hk/record=b5890631; http://repository.lib.cuhk.edu.hk/en/item/cuhk-323512

by Lam Kwan Hang. === Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. === Includes bibliographical references (leaves 75-76). === Abstracts in English and Chinese. === Chapter 1 --- Introduction --- p.5 === Chapter 2 --- Maps into locally compact Riemannian complex --- p.8 === Chapter 2.1 --- Exitsence of energy minimizing maps --- p.8 === Chapter 2.2 --- Length minimizing curves --- p.10 === Chapter 3 --- Harmonic maps into nonpositively curved spaces --- p.13 === Chapter 3.1 --- Nonpositively curved spaces --- p.13 === Chapter 3.2 --- Properties of the distance function --- p.16 === Chapter 4 --- Basic properties of harmonic maps into NPC spaces --- p.21 === Chapter 4.1 --- Monotonicity formula --- p.21 === Chapter 4.2 --- Approximately differentiable maps --- p.24 === Chapter 4.3 --- Local properties of harmonic maps --- p.28 === Chapter 5 --- Existence and uniqueness of harmonic maps in a ho- motopy class --- p.33 === Chapter 5.1 --- Convexity properties of the energy functional --- p.33 === Chapter 5.2 --- Existence and Uniqueness Theorem --- p.37 === Chapter 6 --- Homogeneous approximating maps --- p.40 === Chapter 6.1 --- Regular homogeneous map --- p.40 === Chapter 6.2 --- Homogeneous approximating map --- p.46 === Chapter 7 --- More results on regularity --- p.52 === Chapter 7.1 --- Intrinsically differentiable maps --- p.52 === Chapter 7.2 --- Good homogeneous approximating map --- p.62 === Chapter 8 --- Harmonic maps into building-like complexes --- p.65 === Chapter 8.1 --- F-connected complex --- p.65 === Chapter 8.2 --- Regularity and the Bochner technique --- p.66 === Bibliography --- p.75