dc.contributor.advisor | Verma, Kaushal | |
dc.contributor.author | Ram Mohan, Devang S | |
dc.date.accessioned | 2017-12-10T08:22:15Z | |
dc.date.accessioned | 2018-07-31T06:09:07Z | |
dc.date.available | 2017-12-10T08:22:15Z | |
dc.date.available | 2018-07-31T06:09:07Z | |
dc.date.issued | 2017-12-10 | |
dc.date.submitted | 2014 | |
dc.identifier.uri | https://etd.iisc.ac.in/handle/2005/2890 | |
dc.identifier.abstract | http://etd.iisc.ac.in/static/etd/abstracts/3752/G26306-Abs.pdf | en_US |
dc.description.abstract | In the first chapter of this report, our aim is to introduce harmonic maps between Riemann surfaces using the Energy integral of a map. Once we have the desired prerequisites, we move on to show how to continuously deform a given map to a harmonic map (i.e., find a harmonic map in its homotopy class). We follow J¨urgen Jost’s approach using classical potential theory techniques. Subsequently, we analyze the additional conditions needed to ensure a certain uniqueness property of harmonic maps within a given homotopy class. In conclusion, we look at a couple of applications of what we have shown thus far and we find a neat proof of a slightly weaker version of Hurwitz’s Automorphism Theorem.
In the second chapter, we introduce the concept of minimal surfaces. After exploring a few examples, we mathematically formulate Plateau’s problem regarding the existence of a soap film spanning each closed, simple wire frame and discuss a solution. In conclusion, a partial result (due to Rad´o) regarding the uniqueness of such a soap film is discussed. | en_US |
dc.language.iso | en_US | en_US |
dc.relation.ispartofseries | G26306 | en_US |
dc.subject | Minimal Surfaces | en_US |
dc.subject | Riemann Surfaces | en_US |
dc.subject | Harmonic Maps | en_US |
dc.subject | Plateau's Problem | en_US |
dc.subject | Riemannian Metric | en_US |
dc.subject | Hilbert Space | en_US |
dc.subject | Sobolev Space | en_US |
dc.subject | Energy of a Map | en_US |
dc.subject | Weingarten Map | en_US |
dc.subject | Catenoid | en_US |
dc.subject | Helicoid | en_US |
dc.subject | Enneper Surface | en_US |
dc.subject | Hurwitz's Automorphism Theorem | en_US |
dc.subject.classification | Geometry | en_US |
dc.title | An Introduction to Minimal Surfaces | en_US |
dc.type | Thesis | en_US |
dc.degree.name | MS | en_US |
dc.degree.level | Masters | en_US |
dc.degree.discipline | Faculty of Science | en_US |