Given 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.
| Identifer | oai:union.ndltd.org:bu.edu/oai:open.bu.edu:2144/14007 |
| Date | 09 November 2015 |
| Creators | Gold, Dara |
| Source Sets | Boston University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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