Geodesic
Monotone measures with bad tangential behavior in the plane
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 3, pp. 317-339.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We show that for every $\varepsilon > 0$, there is a set $A\subset \mathbb R^2$ such that $\mathcal H^1 \llcorner A$ is a monotone measure, the corresponding tangent measures at the origin are not unique and $\mathcal H^1 \llcorner A$ has the $1$-dimensional density between $1$ and $3+\varepsilon $ everywhere on the support.
Classification : 49J45
Keywords: monotone measure; monotonicity formula; tangent measure 
@article{CMUC_2011__52_3_a0,
     author = {\v{C}ern\'y, Robert and Kol\'a\v{r}, Jan and Rokyta, Mirko},
     title = {Monotone measures with bad tangential behavior in the plane},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {317--339},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {2011},
     mrnumber = {2843226},
     zbl = {1249.49019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2011__52_3_a0/}
}
TY  - JOUR
AU  - Černý, Robert
AU  - Kolář, Jan
AU  - Rokyta, Mirko
TI  - Monotone measures with bad tangential behavior in the plane
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2011
SP  - 317
EP  - 339
VL  - 52
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2011__52_3_a0/
LA  - en
ID  - CMUC_2011__52_3_a0
ER  - 
%0 Journal Article
%A Černý, Robert
%A Kolář, Jan
%A Rokyta, Mirko
%T Monotone measures with bad tangential behavior in the plane
%J Commentationes Mathematicae Universitatis Carolinae
%D 2011
%P 317-339
%V 52
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2011__52_3_a0/
%G en
%F CMUC_2011__52_3_a0
Černý, Robert; Kolář, Jan; Rokyta, Mirko. Monotone measures with bad tangential behavior in the plane. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 3, pp. 317-339. http://geodesic.mathdoc.fr/item/CMUC_2011__52_3_a0/