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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

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A characterization of revolution quadrics by a system of partial differential equations
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by Vladimir I. Oliker PDF
Proc. Amer. Math. Soc. 138 (2010), 4075-4080 Request permission

Abstract:

It is shown that existence of a global solution to a particular nonlinear system of second order partial differential equations on a complete connected Riemannian manifold has topological and geometric implications and that in the domain of positivity of such a solution, its reciprocal is the radial function of only one of the following rotationally symmetric hypersurfaces in ${\mathbb R}^{n+1}$: paraboloid, ellipsoid, one sheet of a two-sheeted hyperboloid, and a hyperplane.
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Additional Information
  • Vladimir I. Oliker
  • Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
  • Email: oliker@mathcs.emory.edu
  • Received by editor(s): June 6, 2008
  • Received by editor(s) in revised form: February 20, 2009
  • Published electronically: June 29, 2010
  • Additional Notes: The research of the author was partially supported by National Science Foundation grant DMS-04-05622.
  • Communicated by: Matthew J. Gursky
  • © Copyright 2010 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 4075-4080
  • MSC (2010): Primary 53A05, 53C40
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10439-2
  • MathSciNet review: 2679628