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Title:Saddle Surfaces
Author(s):Kalikakis, Dimitrios Emmanuel
Doctoral Committee Chair(s):Igor G. Nikolaev
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:The notion of a saddle surface is well known in Euclidean space. In this work we extend the idea of a saddle surface to geodesically connected metric spaces. We prove that every energy minimizing surface in a nonpositively curved Aleksandrov's space is a saddle surface. Further, we show that the notion of a saddle surface is well defined for, a general Frechet surface and we prove that the space of saddle surfaces in an reals0 domain is complete in the Frechet distance. We also prove a compactness theorem for saddle surfaces in realskappa domains; in spaces of constant curvature we obtain a stronger result based on an isoperimetric inequality for a saddle surface. Finally, we show that a saddle surface in a three-dimensional space of nonzero constant curvature kappa is a space of curvature not greater than kappa in the sense of A. D. Aleksandrov, which generalizes a classical theorem by S. Z. Shefel'.
Issue Date:2000
Type:Text
Language:English
Description:78 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.
URI:http://hdl.handle.net/2142/86989
Other Identifier(s):(MiAaPQ)AAI9955633
Date Available in IDEALS:2015-09-28
Date Deposited:2000


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