Concentrated monotone measures with non-unique tangential behavior in $\mathbb{R}^3$

Title:

Concentrated monotone measures with non-unique tangential behavior in $\mathbb{R}^3$

Creator:

Černý, Robert, Kolář, Jan, and Rokyta, Mirko

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:1481ed3a-c4ab-440c-9527-2c09d359ac49
uuid:1481ed3a-c4ab-440c-9527-2c09d359ac49

Subject:

monotone measure, monotonicity formula, and tangent measure

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1141-1167

Source:

Czechoslovak Mathematical Journal | 2011 Volume:61 | Number:4

Harvested from:

CDK

Metadata only:

false