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Branching solutions to one-dimensional variational problems /
This study deals with the new class of one-dimensional variational problems - the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) it investigates extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; River Edge, NJ :
World Scientific,
©2001.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Ch. 1. Preliminary results. 1.1. Graphs. 1.2. Parametric networks. 1.3. Network-traces. 1.4. Stating of variational problem
- ch. 2. Networks extremality criteria. 2.1. Local structure of extreme parametric networks. 2.2. Local structure of extreme networks-traces
- ch. 3. Linear networks in [symbol]. 3.1. Mutually parallel linear networks with a given boundary. 3.2. Geometry of planar linear trees. 3.3. On the proof of Theorem
- ch. 4. Extremals of length type functionals: the case of parametric networks. 4.1. Parametric networks extreme with respect to Riemannian length functional. 4.2. Local structure of weighted extreme parametric networks. 4.3. Polyhedron of extreme weighted networks in space, having some given type and boundary. 4.4. Global structure of planar extreme weighted trees. 4.5. Geometry of planar embedded extreme weighted binary trees
- ch. 5. Extremals of the length functional: the case of networks
- traces. 5.1. Minimal networks on Euclidean plane. 5.2. Closed minimal networks on closed surfaces of constant curvature. 5.3. Closed local minimal networks on surfaces of polyhedra. 5.4. M.V. Pronin. Morse indices of local minimal networks. 5.5. G.A. Karpunin. Morse theory for planar linear networks
- ch. 6. Extremals of functionals generated by norms. 6.1. Norms of general form. 6.2. Stability of extreme binary trees under deformations of the boundary. 6.3. Planar norms with strictly convex smooth circles. 6.4. Manhattan local minimal and extreme networks.