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Convex Geometry
Csaba Vincze (2013)
University of Debrecen
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13. fejezet - Acknowledgement
13. fejezet -
Acknowledgement
Supported by TÁMOP-4.1.2.A/1-11/1.
table of contents
data sheet
Convex Geometry
Előszó
Introduction
Elements
1.1 Linear Algebra
1.2 Topology
1.3 Affine and convex sets
1.4 Operations with sets
1.5 The Hausdorff distance
1.6 Convex functions
1.7 Excercises
Carathéodory's theorem
2.1 Affinely dependence and independence
2.2 Carathéodory's theorem
2.3 The colorful Carathéodory's theorem
2.4 Excercises
Helly's theorem
3.1 Radon's lemma
3.2 Tverberg's theorem
3.3 Helly's theorem
3.4 Excercises
Generalizations and Applications
4.1 Helly's theorem: generalizations and applications
4.2 Universal covers and approximately central symmetry
4.3 A sandwich theorem
4.4 Excercises
Krasnosselsky's art gallery theorem
5.1 Krasnosselsky's art gallery theorem
5.2 Excercises
Intersections of star-shaped sets
6.1 Intersections of star-shaped sets
6.2 Excercises
Separating and supporting hyperplanes
7.1 Separating and supporting hyperplanes
7.2 Krein-Milman's theorem
7.3 Support functions and Minkowski functionals
7.4 Excercises
Kirchberger's separation theorem
8.1 Kirchberger's separation theorem
8.2 Separation by spherical surfaces
8.3 The best affine approximation
8.4 Excercises
Convex polytopes and polyhedra
9.1 Vertices, edges, faces
9.2 Euler's and Descartes theorem
9.3 Regular polyhedra
Generalized conics
10.1 A panoramic view
10.2 Special types of generalized conics
10.3 Applications in Geometric Tomography
Erdős-Vincze's theorem
11.1 Polyellipses in the plane
11.2 On the curvature of polyellipses
11.3 Erdős-Vincze's theorem
Rådström's embedding theorem
12.1 Rådström's embedding theorem
Acknowledgement
References
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DC Metadata
Title:
Convex Geometry
Authors:
Csaba Vincze
Publisher:
University of Debrecen
Contributors:
University of Debrecen>
Date
2013.05.28.
Identifier:
[URI]
Sources:
eredeti
Language
English
Coverage:
2013, Hungary