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MiS Preprint
100/2013
On the building dimension of closed cones and Almgren’s stratification principle.
Andrea Marchese
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 then or equal to the largest dimension of a vector space contained is some element of $\mathcal{C}$?
