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arXiv · 1408.2398

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

Andrea Marchese
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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 $\mathcal{C}$ 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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Andrea Marchese. 2014-08-11. On the building dimension of closed cones and Almgren's stratification principle. https://arxiv.org/abs/1408.2398

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