2026-09-24T09:55:33Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/83372022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Daniel J. Kleitman.
Zhang, Lizhao, 1973-
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2005-08-23T19:17:41Z
2005-08-23T19:17:41Z
2002
2002
http://hdl.handle.net/1721.1/8337
50500348
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.
Includes bibliographical references (leaves 59-60).
Given a degenerate (n + 1)-simplex in a n-dimensional Euclidean space Rn, which is embedded in a (n + 1)-dimensional Euclidean space Rn+l. We allow all its vertices to have continuous motion in the space, either in Rn+l or restricted in Rn. For a given k, based on certain rules, we separate all its k-faces into 2 groups. During the motion, we give the following restriction: the volume of the k-faces in the 1st group can not increase (these faces are called "k-cables"); the volume of the k-faces in the 2nd group can not decrease ("k-struts"). We will prove that, under more conditions, all the volumes of the k-faces will be preserved for any sufficiently small motion. We also partially generalize the above result to spherical space Sn and hyperbolic space Hn.
by Lizhao Zhang.
Ph.D.
60 leaves
3229421 bytes
3229179 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Rigidity and invariance properties of certain geometric frameworks
Thesis
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Publication
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unknown
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