Hausdorff dimension of Cantor sets and polynomial hulls
HTML articles powered by AMS MathViewer
- by Burglind Jöricke PDF
- Proc. Amer. Math. Soc. 134 (2006), 1347-1354 Request permission
Abstract:
We give examples of Cantor sets in $\mathbb {C}^n$ of Hausdorff dimension 1 whose polynomial hulls have non-empty interior.References
- H. Alexander, Polynomial approximation and hulls in sets of finite linear measure in Cn, Amer. J. Math. 93 (1971), 65–74. MR 284617, DOI 10.2307/2373448
- H. Alexander, The polynomial hull of a set of finite linear measure in $\textbf {C}^n$, J. Analyse Math. 47 (1986), 238–242. MR 874052, DOI 10.1007/BF02792540
- Tien-Cuong Dinh and Mark G. Lawrence, Polynomial hulls and positive currents, Ann. Fac. Sci. Toulouse Math. (6) 12 (2003), no. 3, 317–334 (English, with English and French summaries). MR 2030090, DOI 10.5802/afst.1051
- Henkin G.M., Oral communication.
- Burglind Jöricke, A Cantor set in the unit sphere in $\Bbb C^2$ with large polynomial hull, Michigan Math. J. 53 (2005), no. 1, 189–207. MR 2125541, DOI 10.1307/mmj/1114021092
- Rudin W., Function algebras, (Proc. Internat. Sympos., Tulane Univ., 1965), Scott, Foresman, Chicago, IL, 1966.
- Nessim Sibony, Sur la frontière de Shilov des domaines de $\textbf {C}^n$, Math. Ann. 273 (1985), no. 1, 115–121 (French, with English summary). MR 814198, DOI 10.1007/BF01455917
- Gabriel Stolzenberg, Uniform approximation on smooth curves, Acta Math. 115 (1966), 185–198. MR 192080, DOI 10.1007/BF02392207
- A. G. Vituškin, A certain problem of W. Rudin, Dokl. Akad. Nauk SSSR 213 (1973), 14–15 (Russian). MR 0333243
- John Wermer, The hull of a curve in $C^{n}$, Ann. of Math. (2) 68 (1958), 550–561. MR 100102, DOI 10.2307/1970155
Additional Information
- Burglind Jöricke
- Affiliation: Department of Mathematics, Uppsala University, Box 480, S-751 06 Uppsala, Sweden
- Email: joericke@math.uu.se
- Received by editor(s): November 25, 2004
- Published electronically: October 7, 2005
- Communicated by: Mei-Chi Shaw
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1347-1354
- MSC (2000): Primary 32E20; Secondary 46J15, 46J20
- DOI: https://doi.org/10.1090/S0002-9939-05-08102-5
- MathSciNet review: 2199178