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 Title: Warped products of metric spaces of curvature bounded from above Author(s): Chen, Chien-Hsiung Doctoral Committee Chair(s): Bishop, Richard L. Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: In this work we extend the idea of warped products, which was previously defined on smooth Riemannian manifolds, to geodesic metric spaces and prove the analogue of the theorems on spaces with curvature bounded from above.Suppose that function $f\ :\ M\to R\sp{+}$ is continuous and ($M\times\sb{f}\ N,\ d)$ denotes the warped product of two metric spaces $(M,\ d\sb{M})$ and $(N,\ d\sb{N})$. We prove the following main results in this thesis.Theorem. If $(M,\ d\sb{M})$ and $(N,\ d\sb{N})$ are geodesic metric spaces and if $(M\times\sb{f}\ N,\ d)$ has nonpositive curvature, then (1) $(M,\ d\sb{M})$ has nonpositive curvature. (2) $(N,\ d\sb{N})$ has nonpositive curvature if f has a minimum. (3) f is convex.Theorem. Let M be R or a graph. If $(N,\ d\sb{N})$ has nonpositive curvature and $f\ :\ M\to R\sp{+}$ is convex then $(M\times\sb{f}\ N,\ d)$ has nonpositive curvature. Issue Date: 1996 Type: Text Language: English URI: http://hdl.handle.net/2142/22721 ISBN: 9780591197631 Rights Information: Copyright 1996 Chen, Chien-Hsiung Date Available in IDEALS: 2011-05-07 Identifier in Online Catalog: AAI9712222 OCLC Identifier: (UMI)AAI9712222
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