Positively curved surfaces with no tangent support plane

McCuan, John

doi:10.1090/S0002-9939-04-07659-2

Positively curved surfaces with no tangent support plane
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by John McCuan

Proc. Amer. Math. Soc. 133 (2005), 263-273

DOI: https://doi.org/10.1090/S0002-9939-04-07659-2

Published electronically: August 24, 2004

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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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