Calculus of Variations and Geometric Measure Theory

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 $\mathcal{C}$?