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Quasihyperbolic Distance, Pointed Gromov-Hausdorff Distance, and Bounded Uniform Convergence

Richard, Abigail H.
http://orcid.org/0000-0002-2215-8445
http://rave.ohiolink.edu/etdc/view?acc_num=ucin156086547392659

Abstract Details

2019, PhD, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
We present relationships between various types of convergence. In particular, we examine several types of convergence of sets including Hausdorff convergence, Gromov-Hausdorff convergence, etc. In studying these relationships, we also gain a better understanding of the necessary conditions for certain conformal metric distances to pointed Gromov-Hausdorff converge. We use pointed Gromov-Hausdorff convergence to develop approximations of the quasihyperbolic, Ferrand, Kulkarni-Pinkall-Thurston, and hyperbolic distances via spaces with only finitely many boundary points.
David Herron, Ph.D. (Committee Chair)
Michael Goldberg, Ph.D. (Committee Member)
Nageswari Shanmugalingam, Ph.D. (Committee Member)
Marie A. Snipes, Ph.D. (Committee Member)
Gareth Speight, Ph.D. (Committee Member)
97 p.
Mathematics
Quasihyperbolic; Hausdorff; Gromov-Hausdorff; Ferrand; Kulkarni-Pinkall; Hyperbolic

Recommended Citations

Citations

  • Richard, A. H. (2019). Quasihyperbolic Distance, Pointed Gromov-Hausdorff Distance, and Bounded Uniform Convergence [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin156086547392659

    APA Style (7th edition)

  • Richard, Abigail. Quasihyperbolic Distance, Pointed Gromov-Hausdorff Distance, and Bounded Uniform Convergence. 2019. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin156086547392659.

    MLA Style (8th edition)

  • Richard, Abigail. "Quasihyperbolic Distance, Pointed Gromov-Hausdorff Distance, and Bounded Uniform Convergence." Doctoral dissertation, University of Cincinnati, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin156086547392659

    Chicago Manual of Style (17th edition)

ucin156086547392659
416
© 2019, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.