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Bishop, Richard L. Chen, Chien-Hsiung 2011-05-07T13:49:16Z 2011-05-07T13:49:16Z 10000-01-01 1996 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. Made available in DSpace on 2011-05-07T13:49:16Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9712222.pdf: 1476789 bytes, checksum: 78a6be85e1308b7527d57884c3e17dc6 (MD5) Previous issue date: 1996 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:59:33Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:28:06-05:00 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 9780591197631 AAI9712222 (UMI)AAI9712222 http://hdl.handle.net/2142/22721 eng Copyright 1996 Chen, Chien-Hsiung Mathematics Warped products of metric spaces of curvature bounded from above text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.