This thesis concerns the study of the Cheeger constant of two related hyperbolic Riemann surfaces. The first surface R is formed by taking the quotient U2/Γ(4), where U2 is the upper half-plane model of the hyperbolic plane and Γ(4) is a congruence subgroup of PSL2(Z), an isometry group of U2 . This quotient is shown to form a Riemann surface which is constructed by gluing sides of a fundamental domain for Γ(4) together according to certain specified side pairings. To form the related Riemann surface R' , we follow a similar procedure, this time taking the quotient U2/G, where G is an index 2 subgroup of Γ(4). For both R and R' , we provide an estimate of the Cheeger constant using a procedure given in [2]. The Cheeger constant is believed to be the same for both surfaces.
Date of Award | 2021 |
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Original language | American English |
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Awarding Institution | - Eastern Illinois University
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Supervisor | Grant Lakeland (Supervisor) |
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Cheeger Constants of Two Related Hyperbolic Riemann Surfaces
Hoagland, R. (Author). 2021
Student thesis: Master's Thesis › Master of Arts (MA)