Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Positively curved surfaces with no tangent support plane
HTML articles powered by AMS MathViewer

by John McCuan PDF
Proc. Amer. Math. Soc. 133 (2005), 263-273 Request permission

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.
References
  • Stephanie Alexander and Mohammad Ghomi, The convex hull property and topology of hypersurfaces with nonnegative curvature, Adv. Math. 180 (2003), no. 1, 324–354. MR 2019227, DOI 10.1016/S0001-8708(03)00006-9
  • M. do Carmo and E. Lima, Immersions of manifolds with non-negative sectional curvatures, Bol. Soc. Brasil. Mat. 2 (1971), no. 2, 9–22. MR 328828, DOI 10.1007/BF02584681
  • Mohammad Ghomi, Strictly convex submanifolds and hypersurfaces of positive curvature, J. Differential Geom. 57 (2001), no. 2, 239–271. MR 1879227
  • J. Hadamard, Sur certaines proprietés des trajectoires en dynamique, J. Math. Pures Appl. 3 (1897), 331–387.
  • Shing-Tung Yau, Open problems in geometry, Differential geometry: partial differential equations on manifolds (Los Angeles, CA, 1990) Proc. Sympos. Pure Math., vol. 54, Amer. Math. Soc., Providence, RI, 1993, pp. 1–28. MR 1216573
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53A05
  • Retrieve articles in all journals with MSC (2000): 53A05
Additional Information
  • John McCuan
  • Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
  • Email: mccuan@math.gatech.edu
  • 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
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 263-273
  • MSC (2000): Primary 53A05
  • DOI: https://doi.org/10.1090/S0002-9939-04-07659-2
  • MathSciNet review: 2086219