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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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