Thread-wire surfaces

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.

Bibliographic Details
Main Author: Stephens, Benjamin K. (Benjamin Keith)
Other Authors: David S. Jerison.
Format: Thesis
Language:eng
Published: Massachusetts Institute of Technology 2006
Subjects:
Online Access:http://hdl.handle.net/1721.1/34550
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author Stephens, Benjamin K. (Benjamin Keith)
author2 David S. Jerison.
author_facet David S. Jerison.
Stephens, Benjamin K. (Benjamin Keith)
author_sort Stephens, Benjamin K. (Benjamin Keith)
collection MIT
description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
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spelling mit-1721.1/345502019-04-12T09:19:03Z Thread-wire surfaces Stephens, Benjamin K. (Benjamin Keith) David S. Jerison. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006. Includes bibliographical references (p. 183-190) and Index. This thesis studies surfaces which minimize area, subject to a fixed boundary and to a free boundary with length constraint. Based on physical experiments, I make two conjectures. First, I conjecture that minimizers supported on generic wires have finitely many surface components. I approach this conjecture by proving that surface components of near-wire minimizers are Lipschitz graphs in wire Frenet coordinates, and appear near maxima of wire curvature. Second, I conjecture and prove that surface components of near-wire minimizers are C1 at corners where the thread touches the wire interior. Moreover, the limit of the surface normal field is the Frenet binormal of the wire at the corner point. This shows local wire geometry dominates global wire geometry in influencing the surface corner. Third, I show that these two conjectures are related: assuming additional regularity up to the corner, the finiteness conjecture follows. by Benjamin K. Stephens. Ph.D. 2006-11-07T12:54:38Z 2006-11-07T12:54:38Z 2006 2006 Thesis http://hdl.handle.net/1721.1/34550 71015962 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 190 p. 13231503 bytes 13230927 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology
spellingShingle Mathematics.
Stephens, Benjamin K. (Benjamin Keith)
Thread-wire surfaces
title Thread-wire surfaces
title_full Thread-wire surfaces
title_fullStr Thread-wire surfaces
title_full_unstemmed Thread-wire surfaces
title_short Thread-wire surfaces
title_sort thread wire surfaces
topic Mathematics.
url http://hdl.handle.net/1721.1/34550
work_keys_str_mv AT stephensbenjaminkbenjaminkeith threadwiresurfaces