The Kähler-Ricci Flow on Riemann Surfaces
| Field | Value | Language |
| dc.contributor.author | Nakhoul, John | |
| dc.date.accessioned | 2015-12-02 | |
| dc.date.available | 2015-12-02 | |
| dc.date.issued | 2015-12-01 | |
| dc.identifier.uri | http://hdl.handle.net/2123/14099 | |
| dc.description.abstract | Abstract: In this work we provide a solution to the problem of finding constant curvature metrics on compact Riemann surfaces. Our approach makes full use of the Kähler-Ricci flow equation which is reduced to a PDE of scalar functions by exploiting the hidden Kähler structure on a Riemann surface. The idea is that the Kähler-Ricci flow acts to smooth the metric over time, eventually yielding a metric with constant curvature; and the process of proving this involves analysing the reduced PDE of scalar functions : there one has at their disposal the highly developed theory of parabolic PDEs of which there is an extensive body of knowledge to draw from. | en_AU |
| dc.rights | The author retains copyright of this thesis. It may only be used for the purposes of research and study. It must not be used for any other purposes and may not be transmitted or shared with others without prior permission. | en_AU |
| dc.subject | Kähler, Ricci, Surface | en_AU |
| dc.title | The Kähler-Ricci Flow on Riemann Surfaces | en_AU |
| dc.type | Thesis | en_AU |
| dc.date.valid | 2015-01-01 | en_AU |
| dc.type.thesis | Doctor of Philosophy | en_AU |
| usyd.faculty | Faculty of Science, School of Mathematics and Statistics | en_AU |
| usyd.degree | Doctor of Philosophy Ph.D. | en_AU |
| usyd.awardinginst | The University of Sydney | en_AU |
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