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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Positively curved surfaces with no tangent support plane


Author: John McCuan
Journal: Proc. Amer. Math. Soc. 133 (2005), 263-273
MSC (2000): Primary 53A05
Published electronically: August 24, 2004
MathSciNet review: 2086219
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Abstract: We discuss a characterization of positively curved surfaces $M$with the property that, at each point, the tangent plane to $M$ is not a support plane for the entire surface. Such positively curved surfaces with no tangent support plane necessarily have non-empty boundary, and any portion $B\subset \partial M$ which has convex hull equal to the convex hull of $\partial M$ we call a generating set. This set plays a key role in constructing examples. We give various examples among which there is an embedded topological disk with smallest possible generating set.


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Additional Information

John McCuan
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: mccuan@math.gatech.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07659-2
PII: S 0002-9939(04)07659-2
Received by editor(s): March 15, 2002
Published electronically: August 24, 2004
Additional Notes: Parts of this work were carried out with funding from the National Science Foundation at the University of California, Berkeley, the Mathematical Sciences Research Institute, and Georgia Institute of Technology.
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.