Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/approximation-of-smooth-convex-bodies-bycircumscribed-polytopes-with-MBwfeiRjn8
References (37)
-
S. Glasauer, R. Schneider (1996)
Asymptotic approximation of smooth convex bodies by polytopes, 8
-
S. Glasauer, P. Gruber (1997)
Asymptotic estimates for best and stepwise approximation of convex bodies III, 9
-
R. Schneider (1993)
Convex Bodies—The Brunn-Minkowski Theory -
M. Ludwig (1999)
Asymptotic approximation of smooth convex bodies by general polytopesMathematika, 46
-
P. Gruber (1993)
Aspects of Approximation of Convex Bodies -
K. Leichtweiss (1998)
Affine geometry of convex bodies -
P.M. Gruber (1997)
Comparisons of best and random approximation of convex bodies by polytopesRend. Circ. Mat. Palermo, 50
-
Károly Böröczky, Tick, K. Böröczky
Institute for Mathematical Physics Typical Faces of Best Approximating Three–polytopes Typical Faces of Best Approximating Three-polytopes -
K. Böröczky (2000)
Approximation of General Smooth Convex BodiesAdvances in Mathematics, 153
-
F. Aurenhammer (1987)
Power Diagrams: Properties, Algorithms and ApplicationsSIAM J. Comput., 16
-
P. Gruber (1990)
Volume Approximation of Convex Bodies by Circumscribed Polytopes -
G. Tóth (2004)
Packing and Covering -
P.M. Gruber (2002)
Optimale QuantisierungMath. Semesterber., 49
-
L. Tóth (1953)
Lagerungen in der Ebene auf der Kugel und im RaumThe Mathematical Gazette, 39
-
H. Coxeter (1954)
Review: L. Fejes Tóth, Lagerungen in der Ebene, auf der Kugel und im RaumBulletin of the American Mathematical Society, 60
-
P.M. Gruber (1991)
Applied Geometry and Discrete Mathematics -
(1975)
Vitale: Polygonal approximation of plane convex bodies -
K. Böröczky, B. Csikós (2010)
A new version of l. Fejes Tóth’s moment theoremStudia Scientiarum Mathematicarum Hungarica, 47
-
T. Bonnesen, W. Fenchel, L. Boron, Charles Christenson, B. Smith (1988)
Theory of Convex Bodies -
(1987)
Fenchel: Theory of convex bodies -
P. Gruber, P. Kenderov (1982)
Approximation of convex bodies by polytopesRendiconti del Circolo Matematico di Palermo, 31
-
P. Gruber (2007)
Convex and Discrete Geometry -
D. McClure, R. Vitale (1975)
Polygonal approxi-mation of plane convex bodies -
J. Sangwine-Yager (1995)
A generalization of outer parallel sets of a convex set, 123
-
R. Schneider (1993)
Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition -
(2002)
Stability of some inequalities for threepolyhedra, Rend -
P. Gruber (1993)
Asymptotic estimates for best and stepwise approximation of convex bodies II, 5
-
P. Gruber (2002)
Error of Asymptotic Formulae for Volume Approximation of Convex Bodies inMonatshefte für Mathematik, 135
-
C.A. Rogers (1970)
Hausdorff Measure -
K. Falconer (1985)
The geometry of fractal sets: Contents -
P. Gruber (2004)
Optimum Quantization and Its ApplicationsAdvances in Mathematics, 186
-
P. Zador (1982)
Asymptotic quantization error of continuous signals and the quantization dimensionIEEE Trans. Inf. Theory, 28
-
P.M. Gruber (1993)
Handbook of Convex Geometry A -
(2007)
Wintsche: Typical faces of best approximating three-polytopes, Beit -
K.J. Falconer (1985)
The Geometry of Fractal Sets -
K. Böröczky, M. Reitzner (2004)
Approximation of smooth convex bodies by random circumscribed polytopesAnnals of Applied Probability, 14
-
E. Bronshteyn, L. Ivanov (1975)
The approximation of convex sets by polyhedraSiberian Mathematical Journal, 16
- Publisher
- Springer Journals
- Copyright
- Copyright © 2009 by Mathematisches Seminar der Universität Hamburg and Springer
- Subject
- Mathematics; Geometry ; Topology; Number Theory; Combinatorics; Differential Geometry; Algebra
- ISSN
- 0025-5858
- eISSN
- 1865-8784
- DOI
- 10.1007/s12188-009-0023-2
- Publisher site
- See Article on Publisher Site
Abstract
Let K be a convex body with C 2 boundary in the Euclidean d-space. Following the work of L. Fejes Tóth, R. Vitale, R. Schneider, P.M. Gruber, S. Glasauer and M. Ludwig, best approximation of K by polytopes of restricted number of vertices or facets is well-understood if the approximation is with respect to the volume or the mean width. In this paper we consider the circumscribed polytope P (n) of n facets with minimal surface area, and present an asymptotic formula in terms of n for the difference of surface areas of P (n) and K.
Journal
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: May 26, 2009