Author:
Ward D. J.,Reifenberg E. R.
Abstract
In area theory, Hausdorff measure has been mainly used in the form of Hausdorff ‘spherical’ measure (l) in spite of the fact that work on the geometry of sets of points has mainly used Hausdorff ‘convex’ measure (2,4). The reason for this lies in the inequality This inequality is known (1,3) when the measures are interpreted aslspherical’. But as has for some time been conjectured and this paper shows, with the proper normalization it is false for the convex case.
Publisher
Cambridge University Press (CUP)
Cited by
3 articles.
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1. Existence and soap film regularity of solutions to Plateau’s problem;Advances in Calculus of Variations;2016-10-01
2. A Gross measure property;Transactions of the American Mathematical Society;1978
3. On convex sets and measures;Mathematical Proceedings of the Cambridge Philosophical Society;1966-01