On the building dimension of closed cones and Almgren’s stratification principle.

Andrea Marchese

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Submission date: 05. Nov. 2013
Pages: 9
published in: Proceedings of the American Mathematical Society, 143 (2015) 7, p. 3041-3046 
DOI number (of the published article): 10.1090/S0002-9939-2015-12497-5
Bibtex
MSC-Numbers: 49Q05, 49Q20
Keywords and phrases: building dimension, stratification
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Abstract:
In this paper we disprove a conjecture stated in [4] on the equality of two notions of dimension for closed cones. Moreover, we answer in the negative to the following question, raised in the same paper. Given a compact family of closed cones and a set S such that every blow-up of S at every point x ∈ S is contained in some element of , is it true that the dimension of S is smaller then or equal to the largest dimension of a vector space contained is some element of ?