The Hexagonal Packing Lemma and Discrete Potential Theory
Canadian mathematical bulletin, Tome 33 (1990) no. 2, pp. 247-252

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

One of the questions concerning the Hexagonal Packing Lemma ([1], [3], [4]) is the rate of convergence of Sn . It was suggested in [3] and [4] that Sn = 0(1/n). In the following we prove this conjecture under the additional condition of some "nice" behaviour of the "circle function".
DOI : 10.4153/CMB-1990-039-5
Mots-clés : 30C35, 31C20
Aharonov, Dov. The Hexagonal Packing Lemma and Discrete Potential Theory. Canadian mathematical bulletin, Tome 33 (1990) no. 2, pp. 247-252. doi: 10.4153/CMB-1990-039-5
@article{10_4153_CMB_1990_039_5,
     author = {Aharonov, Dov},
     title = {The {Hexagonal} {Packing} {Lemma} and {Discrete} {Potential} {Theory}},
     journal = {Canadian mathematical bulletin},
     pages = {247--252},
     year = {1990},
     volume = {33},
     number = {2},
     doi = {10.4153/CMB-1990-039-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-039-5/}
}
TY  - JOUR
AU  - Aharonov, Dov
TI  - The Hexagonal Packing Lemma and Discrete Potential Theory
JO  - Canadian mathematical bulletin
PY  - 1990
SP  - 247
EP  - 252
VL  - 33
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-039-5/
DO  - 10.4153/CMB-1990-039-5
ID  - 10_4153_CMB_1990_039_5
ER  - 
%0 Journal Article
%A Aharonov, Dov
%T The Hexagonal Packing Lemma and Discrete Potential Theory
%J Canadian mathematical bulletin
%D 1990
%P 247-252
%V 33
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-039-5/
%R 10.4153/CMB-1990-039-5
%F 10_4153_CMB_1990_039_5

[1] 1. Bárány, Z. Furedi, and Pach, J. Discrete convex functions and proof of the six circle conjecture of Fejes Töth. Can. J. Math. 36 (1984), 569–576. Google Scholar

[2] 2. Duffin, R. J. Discrete Potential Theory. Duke Math. J. 20 (1953), 233–251. Google Scholar

[3] 3. Rodin, B. Schwarz's Lemma for Circle Packings. Invent. Math. 89 (1987), 271–289. Google Scholar

[4] 4. Rodin, B. Schwarz's Lemma for Circle Packings, II, preprint. (1988). Google Scholar

[5] 5. Rodin, B. and Sullivan, D. The Convergence of Circle Packings to the Riemann Mappings. J. Differential Geometry 26 (1987), 349–360. Google Scholar

Cité par Sources :