Geodesic
Quasisymmetrically Minimal Moran Sets
Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 292-305

Voir la notice de l'article provenant de la source Cambridge University Press

M. Hu and S. Wen considered quasisymmetrically minimal uniform Cantor sets of Hausdorff dimension 1, where at the $K$ -th set one removes from each interval $I$ a certain number ${{n}_{k}}$ of open subintervals of length ${{c}_{k}}\left| I \right|$ , leaving $\left( {{n}_{k}}\,+\,1 \right)$ closed subintervals of equal length. Quasisymmetrically Moran sets of Hausdorff dimension 1 considered in the paper are more general than uniform Cantor sets in that neither the open subintervals nor the closed subintervals are required to be of equal length.
DOI : 10.4153/CMB-2011-164-2
Mots-clés : 28A80, 54C30, quasisymmetric, Moran set, Hausdorff dimension 
Dai, Mei-Feng. Quasisymmetrically Minimal Moran Sets. Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 292-305. doi: 10.4153/CMB-2011-164-2
@article{10_4153_CMB_2011_164_2,
     author = {Dai, Mei-Feng},
     title = {Quasisymmetrically {Minimal} {Moran} {Sets}},
     journal = {Canadian mathematical bulletin},
     pages = {292--305},
     year = {2013},
     volume = {56},
     number = {2},
     doi = {10.4153/CMB-2011-164-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-164-2/}
}
TY  - JOUR
AU  - Dai, Mei-Feng
TI  - Quasisymmetrically Minimal Moran Sets
JO  - Canadian mathematical bulletin
PY  - 2013
SP  - 292
EP  - 305
VL  - 56
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-164-2/
DO  - 10.4153/CMB-2011-164-2
ID  - 10_4153_CMB_2011_164_2
ER  - 
%0 Journal Article
%A Dai, Mei-Feng
%T Quasisymmetrically Minimal Moran Sets
%J Canadian mathematical bulletin
%D 2013
%P 292-305
%V 56
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-164-2/
%R 10.4153/CMB-2011-164-2
%F 10_4153_CMB_2011_164_2

[1] [1] Bishop, C. J., Quasiconformal mappings which increase dimension. Ann. Acad. Sci. Fenn. Math. 24(1999), no. 2, 397–407. Google Scholar

[2] [2] Falconer, K., Fractal Geometry: Mathematical Foundation and Applications. JohnWiley & Sons, Chichester, 1990. Google Scholar

[3] [3] Gehring, F.W. and Väisälä, J., Hausdorff dimension and quasiconformal mappings. Math. J. London Math. Soc. 6(1973), 504-512. Google Scholar | DOI

[4] [4] Hakobyan, H. A., Cantor sets minimal for quasi-symmetric maps. J. Contemp. Math. Anal. 41(2006), no. 2, 5-13. Translated from the Russian. Google Scholar

[5] [5] Hu, M. and Wen, S., Quasisymmetrically minimal uniform Cantor sets. Topology Appl. 155(2008), no. 6, 515–521. Google Scholar | DOI

[6] [6] Hua, S., The dimensions of generalized self-similar sets. (Chinese) Acta. Math. Appl. Sinica 17(1994), no. 4, 551–558. Google Scholar

[7] [7] Kovalev, L. V., Conformal dimension does not assume values between 0 and 1. Duke Math. J. 134(2006), no. 1, 1–13. Google Scholar | DOI

[8] [8] Tukia, P., Hausdorff dimension and quasisymmetric mappings. Math. Scand. 65(1989), no. 1, 152–160. Google Scholar

[9] [9] Tyson, J. T., Sets of minimal Hausdorff dimension for quasisiconformal maps. Proc. Amer. Math. Soc. 128(2000), no. 11, 3361–3367. Google Scholar | DOI

[10] [10] Wu, J. M., Null sets for doubling and dyadic doubling measures. Ann. Acad. Sci. Fenn. Ser. A I Math. 18(1993), no. 1, 77–91. Google Scholar

Cité par Sources :