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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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On the building dimension of closed cones and Almgren’s stratification principle
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by Andrea Marchese PDF
Proc. Amer. Math. Soc. 143 (2015), 3041-3046 Request permission

Abstract:

In this paper we disprove a conjecture stated in Stratification of minimal surfaces, mean curvature flows, and harmonic maps by Brian White on the equality of two notions of dimension for closed cones. Moreover, we answer in the negative the following question, raised in the same paper. Given a compact family $\mathcal {C}$ of closed cones and a set $S$ such that every blow-up of $S$ at every point $x\in S$ is contained in some element of $\mathcal {C}$, is it true that the dimension of $S$ is smaller than or equal to the largest dimension of a vector space contained is some element of $\mathcal {C}$?
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Additional Information
  • Andrea Marchese
  • Affiliation: Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22, 04103 Leipzig, Germany
  • Email: marchese@mis.mpg.de
  • Received by editor(s): November 4, 2013
  • Received by editor(s) in revised form: March 13, 2014
  • Published electronically: February 27, 2015
  • Communicated by: Tatiana Toro
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 3041-3046
  • MSC (2010): Primary 49Q05, 49Q20
  • DOI: https://doi.org/10.1090/S0002-9939-2015-12497-5
  • MathSciNet review: 3336628