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

Voir la notice de l'article dans Czech Digital Mathematics Library

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
Mots-clés : monotone measure; monotonicity formula; tangent measure 
@article{10_1007_s10587_011_0054_6,
     author = {\v{C}ern\'y, Robert and Kol\'a\v{r}, Jan and Rokyta, Mirko},
     title = {Concentrated monotone measures with non-unique tangential behavior in $\mathbb{R}^3$},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1141--1167},
     publisher = {mathdoc},
     volume = {61},
     number = {4},
     year = {2011},
     doi = {10.1007/s10587-011-0054-6},
     mrnumber = {2886262},
     zbl = {1249.53006},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-011-0054-6/}
}
TY  - JOUR
AU  - Černý, Robert
AU  - Kolář, Jan
AU  - Rokyta, Mirko
TI  - Concentrated monotone measures with non-unique tangential behavior in $\mathbb{R}^3$
JO  - Czechoslovak Mathematical Journal
PY  - 2011
SP  - 1141
EP  - 1167
VL  - 61
IS  - 4
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-011-0054-6/
DO  - 10.1007/s10587-011-0054-6
LA  - en
ID  - 10_1007_s10587_011_0054_6
ER  - 
%0 Journal Article
%A Černý, Robert
%A Kolář, Jan
%A Rokyta, Mirko
%T Concentrated monotone measures with non-unique tangential behavior in $\mathbb{R}^3$
%J Czechoslovak Mathematical Journal
%D 2011
%P 1141-1167
%V 61
%N 4
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-011-0054-6/
%R 10.1007/s10587-011-0054-6
%G en
%F 10_1007_s10587_011_0054_6
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. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-011-0054-6/

Cité par Sources :