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2022 Floating bodies and approximation of convex bodies by polytopes
Elisabeth M. Werner
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Probab. Surveys 19: 113-128 (2022). DOI: 10.1214/22-PS5

Abstract

We describe some results on approximation of convex bodies by polytopes. Best and random approximations are considered and compared. The geometric quantities related to the convex body, that appear naturally in such approximation questions are the affine surface areas. Those, and their relation to floating bodies, will be discussed as well.

In this survey we give only a very selective collection of results on approximation by polytopes.

Funding Statement

Partially supported by NSF grants DMS-1811146 and DMS-2103482 and by a Simons Fellowship

Acknowledgments

The author wants to thank the referees for the careful reading and suggestions for improvement.

Citation

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Elisabeth M. Werner. "Floating bodies and approximation of convex bodies by polytopes." Probab. Surveys 19 113 - 128, 2022. https://doi.org/10.1214/22-PS5

Information

Received: 1 October 2021; Published: 2022
First available in Project Euclid: 8 March 2022

Digital Object Identifier: 10.1214/22-PS5

Subjects:
Primary: 52A20 , 52A40 , 60B

Keywords: affine surface area , Floating bodies , Random polytopes

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