Geodesic
Concentrated monotone measures with non-unique tangential behavior in $\mathbb{R}^3$
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 1141-1167

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We show that for every $\varepsilon >0$ there is a set $A\subset \mathbb{R}^3$ such that ${\Cal H}^1\llcorner A$ is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and ${\Cal H}^1\llcorner A$ has the $1$-dimensional density between $1$ and $2+\varepsilon $ everywhere in the support.
DOI : 10.1007/s10587-011-0054-6
Classification : 28A75, 49Q15, 53A10
Keywords: monotone measure; monotonicity formula; tangent measure 
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     title = {Concentrated monotone measures with non-unique tangential behavior in $\mathbb{R}^3$},
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Černý, Robert; Kolář, Jan; Rokyta, Mirko. Concentrated monotone measures with non-unique tangential behavior in $\mathbb{R}^3$. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 1141-1167. doi: 10.1007/s10587-011-0054-6

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