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dc.contributor.authorGold, Daraen_US
dc.date.accessioned2016-01-13T19:51:48Z
dc.date.available2016-01-13T19:51:48Z
dc.date.issued2015
dc.identifier.urihttps://hdl.handle.net/2144/14007
dc.description.abstractGiven an embedding of a closed k-dimensional manifold M into N-dimensional Euclidean space R^N, we aim to perform negative gradient flow of a penalty function P that acts on the space of all smooth embeddings of M into R^N to find an ideal manifold embedding. We study the computation of the gradient for a penalty function that contains both a curvature and distance term. We also find a lower bound for how long an embedding will remain in the space of embeddings when moving in a fixed, normal gradient direction. Finally, we study the distance penalty function in a special case in which we can prove short time existence of the negative gradient flow using the Cauchy-Kovalevskaya Theorem.en_US
dc.language.isoen_US
dc.subjectMathematicsen_US
dc.subjectDifferential geometryen_US
dc.subjectEmbeddingsen_US
dc.subjectGradient flowen_US
dc.titleGeometric gradient flow in the space of smooth embeddingsen_US
dc.typeThesis/Dissertationen_US
dc.date.updated2015-11-09T14:25:50Z
etd.degree.nameDoctor of Philosophyen_US
etd.degree.leveldoctoralen_US
etd.degree.disciplineMathematics & Statisticsen_US
etd.degree.grantorBoston Universityen_US


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