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DissertationHoehner-03-30-2016.pdf (288.87 KB)

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The Surface Area Deviation of the Euclidean Ball and a Polytope

Hoehner, Steven Douglas
http://rave.ohiolink.edu/etdc/view?acc_num=case1459355790

Abstract Details

2016, Doctor of Philosophy, Case Western Reserve University, Mathematics.
While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. In this thesis we give upper and lower bounds for the approximation of the Euclidean unit ball by arbitrarily positioned polytopes with a fixed number of vertices or facets in the surface area deviation. The main results of this paper are joint work with Dr. Carsten Schuett and Dr. Elisabeth Werner. In the introduction, we collect some definitions and background material from analysis and convex geometry that will be used throughout the paper. The main results of this dissertation are stated in Chapter 1. In Chapter 2, we collect several results related to our main results. Our focus there will be on results related to best and random approximation with respect to the volume, surface area, and mean width deviations. In Chapter 3 we state several auxiliary lemmas needed for the proofs of our main results. The proofs of our main results are given in Chapters 4 and 5.
Elisabeth Werner (Advisor)
Carsten Schuett (Committee Member)
Woyczynski Wojbor (Committee Member)
Mathur Harsh (Committee Member)
88 p.
Mathematics
convexity; convex body; polytope; approximation; surface area; surface area deviation; Euclidean ball; convex geometry

Recommended Citations

Citations

  • Hoehner, S. D. (2016). The Surface Area Deviation of the Euclidean Ball and a Polytope [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1459355790

    APA Style (7th edition)

  • Hoehner, Steven. The Surface Area Deviation of the Euclidean Ball and a Polytope. 2016. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1459355790.

    MLA Style (8th edition)

  • Hoehner, Steven. "The Surface Area Deviation of the Euclidean Ball and a Polytope." Doctoral dissertation, Case Western Reserve University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=case1459355790

    Chicago Manual of Style (17th edition)

case1459355790
766
© 2016, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.