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On the Volume Product of the Unit Balls of Lipschitz-Free Spaces

Alanazi, Naif Mohammed
http://orcid.org/0009-0008-7362-729X
http://rave.ohiolink.edu/etdc/view?acc_num=kent1729688666198301

Abstract Details

2024, MS, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
In this thesis, we examine the volume product of the unit balls in Lipschitz-free spaces. In particular, we study metric spaces corresponding to different graphs having 3, 4, or 5 vertices. Our analysis involves studying the structure of Lipschitz-free spaces over these graphs. We construct the unit ball in the Lipschitz-free space and find its polar body, i.e., the unit ball in the dual norm. Next, we compute the volumes of the unit ball and the polar body and find the exact value of the volume product of those spaces. We compare the outcome of this computation with the volume product of the unit cube to confirm Mahler’s conjecture for those Lipschitz-free spaces. In this thesis, we also review many essential definitions and facts before presenting examples to support our analysis. This work is based on the fundamental properties of Lipschitz functions and spaces, emphasizing their geometric and algebraic properties.
Artem Zvavitch (Advisor)
Dmitry Ryabogin (Committee Member)
Peter Gordon (Committee Member)
67 p.
Mathematics
Convex bodies; Volume Product; Lipschitz-Free Spaces; Mahler’s conjecture

Recommended Citations

Citations

  • Alanazi, N. M. (2024). On the Volume Product of the Unit Balls of Lipschitz-Free Spaces [Master's thesis, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1729688666198301

    APA Style (7th edition)

  • Alanazi, Naif. On the Volume Product of the Unit Balls of Lipschitz-Free Spaces. 2024. Kent State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=kent1729688666198301.

    MLA Style (8th edition)

  • Alanazi, Naif. "On the Volume Product of the Unit Balls of Lipschitz-Free Spaces." Master's thesis, Kent State University, 2024. http://rave.ohiolink.edu/etdc/view?acc_num=kent1729688666198301

    Chicago Manual of Style (17th edition)

kent1729688666198301
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© 2024, some rights reserved.Creative Commons License On the Volume Product of the Unit Balls of Lipschitz-Free Spaces by Naif Mohammed Alanazi is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Kent State University and OhioLINK.