Files in this item



application/pdf9955633.pdf (3MB)Restricted to U of Illinois
(no description provided)PDF


Title:Saddle Surfaces
Author(s):Kalikakis, Dimitrios Emmanuel
Doctoral Committee Chair(s):Igor G. Nikolaev
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
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
Description:78 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.
Other Identifier(s):(MiAaPQ)AAI9955633
Date Available in IDEALS:2015-09-28
Date Deposited:2000

This item appears in the following Collection(s)

Item Statistics