Windemuth, Arthur (2021):
Surfaces in Homogeneous Manifolds Generated by Schwarz Reflection. (Publisher's Version)
Darmstadt, Technische Universität,
DOI: 10.26083/tuprints-00017641,
[Ph.D. Thesis]
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Item Type: | Ph.D. Thesis | ||||
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Status: | Publisher's Version | ||||
Title: | Surfaces in Homogeneous Manifolds Generated by Schwarz Reflection | ||||
Language: | English | ||||
Abstract: | Given a Jordan curve on the edge set of a total geodesic polytope in Euclidean, spherical, or hyperbolic n-space, we inscribe an embedded surface with boundary of the given curve which lies in the interior of the polytope. By Schwarz reflection, we can extend this surface patch to a complete surfaces. This main result of the thesis gives a necessary and sufficient condition if the resulting surface is embedded or has self-intersections. This problem is a generalisation of the classical construction of the Schwarz D surface and Lawsons surfaces. |
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Place of Publication: | Darmstadt | ||||
Collation: | viii, 208 Seiten | ||||
Classification DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik | ||||
Divisions: | 04 Department of Mathematics > Applied Geometry | ||||
Date Deposited: | 12 Mar 2021 09:25 | ||||
Last Modified: | 12 Mar 2021 09:25 | ||||
DOI: | 10.26083/tuprints-00017641 | ||||
URN: | urn:nbn:de:tuda-tuprints-176419 | ||||
Referees: | Große-Brauckmann, Prof. Dr. Karsten and Mäder-Baumdicker, Prof. Dr. Elena | ||||
Refereed: | 18 December 2020 | ||||
URI: | https://tuprints.ulb.tu-darmstadt.de/id/eprint/17641 | ||||
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