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dc.contributor.advisorVerma, Kaushal
dc.contributor.authorRam Mohan, Devang S
dc.date.accessioned2017-12-10T08:22:15Z
dc.date.accessioned2018-07-31T06:09:07Z
dc.date.available2017-12-10T08:22:15Z
dc.date.available2018-07-31T06:09:07Z
dc.date.issued2017-12-10
dc.date.submitted2014
dc.identifier.urihttps://etd.iisc.ac.in/handle/2005/2890
dc.identifier.abstracthttp://etd.iisc.ac.in/static/etd/abstracts/3752/G26306-Abs.pdfen_US
dc.description.abstractIn 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.isoen_USen_US
dc.relation.ispartofseriesG26306en_US
dc.subjectMinimal Surfacesen_US
dc.subjectRiemann Surfacesen_US
dc.subjectHarmonic Mapsen_US
dc.subjectPlateau's Problemen_US
dc.subjectRiemannian Metricen_US
dc.subjectHilbert Spaceen_US
dc.subjectSobolev Spaceen_US
dc.subjectEnergy of a Mapen_US
dc.subjectWeingarten Mapen_US
dc.subjectCatenoiden_US
dc.subjectHelicoiden_US
dc.subjectEnneper Surfaceen_US
dc.subjectHurwitz's Automorphism Theoremen_US
dc.subject.classificationGeometryen_US
dc.titleAn Introduction to Minimal Surfacesen_US
dc.typeThesisen_US
dc.degree.nameMSen_US
dc.degree.levelMastersen_US
dc.degree.disciplineFaculty of Scienceen_US


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