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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

IMPACT FACTOR 2018: 0.789

CiteScore 2018: 0.73

SCImago Journal Rank (SJR) 2018: 0.329
Source Normalized Impact per Paper (SNIP) 2018: 0.908

Mathematical Citation Quotient (MCQ) 2017: 0.62

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Volume 18, Issue 1


Polytopal approximation of elongated convex bodies

Gilles Bonnet
Published Online: 2018-01-07 | DOI: https://doi.org/10.1515/advgeom-2017-0038


This paper presents bounds for the best approximation, with respect to the Hausdorff metric, of a convex body K by a circumscribed polytope P with a given number of facets. These bounds are of particular interest if K is elongated. To measure the elongation of the convex set, its isoperimetric ratio Vj(K)1/j Vi(K)−1/i is used.

Keywords: Polytopal approximation; elongated convex bodies; isoperimetric ratio; δ-net

MSC 2010: Primary 52A27; 52B11; Secondary 52B60


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About the article

Received: 2015-10-22

Revised: 2016-04-18

Published Online: 2018-01-07

Published in Print: 2018-01-26

Citation Information: Advances in Geometry, Volume 18, Issue 1, Pages 105–114, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2017-0038.

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