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Geometric growth on translation surfaces
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Colognese, Paul (2021) Geometric growth on translation surfaces. PhD thesis, University of Warwick.
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WRAP_Theses_Colognese_2021.pdf - Submitted Version - Requires a PDF viewer. Download (950Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3782256~S15
Abstract
In this thesis we study geometric growth on translation surfaces. We obtain asymptotic formulae for the growth of various geometric objects on translation surfaces such as volumes of balls and circumferences of large circles. Using these asymptotic formulae, we then prove a distribution result for large circles on translation surfaces. Finally, we explore the entropy minimization problem for translation surfaces and prove a special case. These results generalize well-known results that hold for negatively curved surfaces.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Geometry, Surfaces, Entropy, Asymptotic distribution (Probability theory) | ||||
Official Date: | September 2021 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Pollicott, Mark | ||||
Extent: | vi, 119 leaves : illustrations, charts | ||||
Language: | eng |
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