On the level sets of a distance function in a Minkowski space
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- by Ronald Gariepy and W. D. Pepe
- Proc. Amer. Math. Soc. 31 (1972), 255-259
- DOI: https://doi.org/10.1090/S0002-9939-1972-0287442-5
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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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Bibliographic 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