Vrzina, Miroslav (2016):
Constant Mean Curvature Annuli in Homogeneous Manifolds.
Darmstadt, Technische Universität Darmstadt,
[Ph.D. Thesis]
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Item Type: | Ph.D. Thesis | ||||
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Title: | Constant Mean Curvature Annuli in Homogeneous Manifolds | ||||
Language: | English | ||||
Abstract: | In this thesis we construct constant mean curvature annuli in homogeneous manifolds. These annuli generalise cylinders and unduloids in Euclidean space. In the first part we show existence of cylinders in various homogeneous manifolds, for example in Sol or in PSL(2,R). These cylinders are translationally invariant and thus they are solutions of an ordinary differential equation. We use a geometric approach to discuss these equations. In the second part we study the existence problem for tilted unduloids in the product of the hyperbolic plane and the real line. Here we have a proper partial differential equation at hand. We reduce this existence problem to a uniqueness problem for minimal annuli bounded by linked geodesic circles in the Berger spheres. |
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Place of Publication: | Darmstadt | ||||
Classification DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik | ||||
Divisions: | 04 Department of Mathematics > Applied Geometry | ||||
Date Deposited: | 19 May 2016 08:01 | ||||
Last Modified: | 19 May 2016 08:01 | ||||
URN: | urn:nbn:de:tuda-tuprints-54440 | ||||
Referees: | Große-Brauckmann, Prof. Dr. Karsten ; Schneider, PD Dr. Matthias | ||||
Date of oral examination: | 22 April 2016 | ||||
URI: | https://tuprints.ulb.tu-darmstadt.de/id/eprint/5444 | ||||
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