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Petrunin, Anton 10000-01-01 2011-05-07T14:04:30Z 1995 2011-05-07T14:04:30Z Here we generalize quasigeodesics to multidimensional Alexandrov space with curvature bounded from below and prove that classical theorems of Alexandrov also hold for this case. Also we develop gradient curves as a tool for studying spaces with curvature bounded from below. In the second chapter we give some applications of quasigeodesics and gradient curves: the Radius Sphere theorem, the Glueing theorem and the First variation formula for extremal subsets. Made available in DSpace on 2011-05-07T14:04:30Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9543694.pdf: 2461215 bytes, checksum: 946a594e212c7bf3ec4afc358cfa047a (MD5) Previous issue date: 1995 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:02:38Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:29:47-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9543694 (UMI)AAI9543694 http://hdl.handle.net/2142/23166 eng Copyright 1995 Petrunin, Anton Mathematics Quasigeodesics in multidimensional Alexandrov spaces text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.