Harmonic maps and totally geodesic maps between metric spaces. (English) Zbl 1144.53300
Tohoku Mathematical Publications 28. Sendai: Tohoku University, Mathematical Institute (Thesis 2003). iv, 69 p. (2004).
Table of contents: 1. Introduction; 2. CAT(\(K\))-spaces and Alexandrov spaces; 2.1. Definitions; 2.2. First variation formula; 2.3 Foot-points; 3. Totally geodesic maps; 3.1. Basic properties; 3.2. Local isometric splitting; 3.3. Differentiable structure; 3.4. Finslerian and Riemannian structures; 4. Sobolev spaces; 4.1. Upper gradients; 4.2. Minimal generalized upper gradients; 4.3. Dirichlet problem; 4.4. Minimality of Lip\(u\); 4.5. Comparison of Sobolev spaces and its application; 5. Harmonicity of totally geodesic maps; 5.1. Harmonicity; 5.2. Examples.
MSC:
| 53-02 | Research exposition (monographs, survey articles) pertaining to differential geometry |
| 53C45 | Global surface theory (convex surfaces à la A. D. Aleksandrov) |
| 53C60 | Global differential geometry of Finsler spaces and generalizations (areal metrics) |
| 53C20 | Global Riemannian geometry, including pinching |
| 53C43 | Differential geometric aspects of harmonic maps |
