Minimal NetworksThe Steiner Problem and Its GeneralizationsCRC Press, 16 mars 1994 - 432 pages This book focuses on the classic Steiner Problem and illustrates how results of the problem's development have generated the Theory of Minimal Networks, that is systems of "rubber" branching threads of minimal length. This theory demonstrates a brilliant interconnection among differential and computational geometry, topology, variational calculus, and graph theory. All necessary preliminary information is included, and the book's simplified format and nearly 150 illustrations and tables will help readers develop a concrete understanding of the material. All nontrivial statements are proved, and plenty of exercises are included. |
Table des matières
Some Necessary Results from | 1 |
Topological Approach | 24 |
Networks on Manifolds | 56 |
The Steiner Problem | 84 |
Existence Theorems | 97 |
Local Structure of Minimal Networks | 105 |
Global Structure of Minimal Networks | 123 |
Global Minimal Networks on the Plane | 147 |
Expressions et termes fréquents
a₁ adjacent admissible angle Assertion boundary edges boundary vertices branching points called canonical cells characteristic arc characteristic triangle closed minimal network coincides connected components Consider consists construct contains contour convex convex hull Corollary corresponding curvature curve cycle defined Definition deformation Denote domain dual graph e₁ embedded ending edge equals equivalent exists Figure finite flat Klein bottle flat torus H₁ hexagon integers intersection invariant with respect joining Klein bottle Lemma length lies inside linear skeleton mapping metric minimal realization minimal tree n-gon neighborhood nondegenerate obtained oriented pair parametric networks partition planar polygonal line polyhedron problem Proof Proposition prove quasiregular rain regular Riemannian manifold RM-realization semiplane shortest geodesic sides skeleton from WP5 snake Sp(L space spine Steiner network Steiner point Steiner ratio Steiner tree straight line straight segment subset tetrahedron Theorem topological space topology translation trivial network tw(a tw(x twisting number unique vector vertex y₁