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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.

 

On the level sets of a distance function in a Minkowski space
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by Ronald Gariepy and W. D. Pepe PDF
Proc. Amer. Math. Soc. 31 (1972), 255-259 Request permission

Abstract:

Given a closed subset of an $n$-dimensional Minkowski space with a strictly convex or differentiable norm, then, for almost every $r > 0$, the $r$-level set (points whose distance from the closed set is $r$) contains an open subset which is an $n - 1$ dimensional Lipschitz manifold and whose complement relative to the level set has $n - 1$ dimensional Hausdorff measure zero. In case $n = 2$ and the norm is twice differentiable with bounded second derivative, almost every level set is a 1 manifold.
References
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 31 (1972), 255-259
  • MSC: Primary 52.50; Secondary 53.00
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0287442-5
  • MathSciNet review: 0287442