Convex and Discrete GeometrySpringer Science & Business Media, 17.05.2007 - 580 Seiten Convex and Discrete Geometry is an area of mathematics situated between analysis, geometry and discrete mathematics with numerous relations to other areas. The book gives an overview of major results, methods and ideas of convex and discrete geometry and its applications. Besides being a graduate-level introduction to the field, it is a practical source of information and orientation for convex geometers. It should also be of use to people working in other areas of mathematics and in the applied fields. |
Inhalt
Rigidity | 292 |
and the MindingKouchnirenkoBernstein Theorem | 332 |
Geometry of Numbers and Aspects of Discrete Geometry 353 | 352 |
203 | 375 |
Lattice Vector Problem | 417 |
2 | 419 |
for 8L C of MinkowskiHlawka | 448 |
References | 513 |
5 | 149 |
Central Symmetrization and the RogersShephard | 179 |
11 | 202 |
Convex Polytopes | 243 |
Index | 567 |
Author Index | 577 |
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Häufige Begriffe und Wortgruppen
affine algorithm assume ball basis Brunn-Minkowski closed convex coefficients combinatorial compact concluding the proof conjecture consider contains convex body convex cone convex functions convex geometry convex lattice polytopes convex polytopes convex sets Corollary corresponding d x d defined density differentiable dimension discs Ed/L ellipsoid equality Euler exterior normal face facets finite following result fundamental theorem geometry of numbers given Gruber halfspaces Hence holds implies induction integer unimodular intersection Jordan measurable lattice packing lattice point lattice polytopes Lemma linear optimization Math matrix McMullen metric minimum Minkowski Minkowski-Hlawka theorem Minkowski's theorem mixed volumes normal vector number theory orthogonal planar polyhedra polyhedron polynomial problem proper convex body proper convex polytope properties Proposition Sect show the following simplex space sufficient to show suitable support hyperplane symmetric tiling translates valuation vertex vertices yields