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MiS Preprint

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

Andrea Marchese


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 $\mathcal{C}$?

MSC Codes:
49Q05, 49Q20
building dimension, stratification

Related publications

2015 Repository Open Access
Andrea Marchese

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

In: Proceedings of the American Mathematical Society, 143 (2015) 7, pp. 3041-3046