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Cusped hyperbolic 3-manifolds with a compact totally geodesic boundary

Ekanayake, Hasitha Anuradha (2023) Cusped hyperbolic 3-manifolds with a compact totally geodesic boundary. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

This thesis is a study on the volumes of cusped hyperbolic 3-manifolds with a compact totally geodesic boundary. Its main goal is to identify the smallest member in the class of such manifolds. Author outlines a process that zeroes in on a manifold which was preidentified as a candidate for the smallest manifold in this class. Most of the computations are parameterized in terms of $x_1$ ; a variable closely associated with the volumes of manifolds with geodesic boundary. Chapter 3 describes the construction of a lower bound for the volumes of manifolds in $\mathcal{N}_{c,c}$ in terms of their $x_1$ values. In chapter 4, the relation between the geometry of a manifold in $\mathcal{N}_{c,c}$ is leveraged to obtain a lower bound for its $x_1$ value. Results in those two chapters yield an interval of possible $x_1$ values for the smallest manifold in $\mathcal{N}_{c,c}$. The remainder of the thesis investigate this interval extensively.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Ekanayake, Hasitha Anuradhahae20@pitt.eduhae20
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairDeBlois, Jason Cjdeblois@pitt.edu
Committee MemberMartelli, Brunobruno.martelli@unipi.it
Committee MemberGartside, Paulpmg20@pitt.edu
Committee MemberWang-Erickson, Carlcarl.wang-erickson@pitt.edu
Date: 6 September 2023
Date Type: Publication
Defense Date: 26 July 2023
Approval Date: 6 September 2023
Submission Date: 4 August 2023
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 189
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Hyperbolic 3-manifolds, Totally geodesic boundary, Centered Dual Decomposition
Date Deposited: 06 Sep 2023 15:08
Last Modified: 06 Sep 2023 15:08
URI: http://d-scholarship.pitt.edu/id/eprint/45241

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