WEIGHTED FLOATING BODIES AND POLYTOPAL APPROXIMATION

被引：18

作者：

Besau, Florian ^{[1
]}

Ludwig, Monika ^{[2
]}

Werner, Elisabeth M. ^{[3
]}

机构：

[1] Goethe Univ Frankfurt, Inst Math, Robert Mayer Str 10, D-60054 Frankfurt, Germany

[2] Tech Univ Wien, Inst Diskrete Math Geometrie, Wiedner Hauptstr 8-10-1046, A-1040 Vienna, Austria

[3] Case Western Reserve Univ, Dept Math Appl Math & Stat, 10900 Euclid Ave, Cleveland, OH 44106 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 370卷 / 10期

基金：

美国国家科学基金会; 奥地利科学基金会;

关键词：

AFFINE SURFACE; CONVEX-BODIES; STEPWISE APPROXIMATION;

D O I：

10.1090/tran/7233

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Asymptotic results for weighted floating bodies are established and used to obtain new proofs for the existence of floating areas on the sphere and in hyperbolic space and to establish the existence of floating areas in Hilbert geometries. Results on weighted best and random approximation and the new approach to floating areas are combined to derive new asymptotic approximation results on the sphere, in hyperbolic space, and in Hilbert geometries.

引用

页码：7129 / 7148

页数：20

共 20 条

[1] Ulam floating bodies
Huang, Han
Slomka, Boaz A.
Werner, Elisabeth M.
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2019, 100 (02): : 425 - 446
[2] Duality of Floating and Illumination Bodies
Mordhorst, Olaf
Werner, Elisabeth M.
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2020, 69 (05) : 1507 - 1541
[3] Flag numbers and floating bodies
Besau, Florian
Schuett, Carsten
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ADVANCES IN MATHEMATICS, 2018, 338 : 912 - 952
[4] Approximation of smooth convex bodies by random polytopes
Grote, Julian
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ELECTRONIC JOURNAL OF PROBABILITY, 2018, 23
[5] Mechanics of floating bodies
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PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2021, 477 (2255):
[6] Floating and Illumination Bodies for Polytopes: Duality Results
Mordhorst, Olaf
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DISCRETE ANALYSIS, 2019,
[7] Separation bodies: a conceptual dual to floating bodies
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GEOMETRIAE DEDICATA, 2023, 217 (04)
[10] Archimedes' principle of flotation and floating bodies: construction, extensions and related problems
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Zhang, Ning
ACTA MATHEMATICA SCIENTIA, 2025, 45 (01) : 237 - 256

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