Existenz und Nicht-Existenz monotoner Größen für geometrische Flüsse : Potenzen von mittlerer und Gaußscher Krümmung
| Type of Publication: | Dissertation |
| URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-0-298036 |
| Author: | Franzen, Martin |
| Year of publication: | 2015 |
| Summary: |
We explore geometric flow equations. Our main results concern flows by powers of the mean curvature and Gauss curvature. Firstly we prove longtime existence for entire graphs under mild assumptions. Secondly for closed hypersurfaces we show the existence and the non-existence of certain monotone quantities that ensure convergence to round points or convergence to spheres at infinity. Thirdly we prove that pinched hypersurfaces shrink to round points using a computer algebra system.
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| Examination date (for dissertations): | Jul 24, 2015 |
| Dissertation note: | Doctoral dissertation, University of Konstanz |
| Subject (DDC): | 510 Mathematics |
| Keywords: | geometric flow equations, geometric analysis, differential geometry, computer algebra, pde |
| Link to License: | In Copyright |
| Bibliography of Konstanz: | Yes |
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FRANZEN, Martin, 2015. Existenz und Nicht-Existenz monotoner Größen für geometrische Flüsse : Potenzen von mittlerer und Gaußscher Krümmung [Dissertation]. Konstanz: University of Konstanz
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