Calculus of Variations and Geometric Measure Theory
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A. Marchese

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

created by marchese on 22 Oct 2013
modified on 19 Mar 2014


Accepted Paper

Inserted: 22 oct 2013
Last Updated: 19 mar 2014

Journal: Proc. Amer. Math. Soc.
Year: 2013


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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