no. 3
Hulls of subsets of the torus in ℂ 2
Annales de l'Institut Fourier, Tome 48 (1998) no. 3, pp. 785-795.

Nous donnons une construction d’un compact non-polynomialement convexe dans le tore standard de ℂ 2 tel que son enveloppe polynomiale soit sans structure analytique.

We construct a non-polynomially convex compact subset of the unit torus in ℂ 2 with polynomially convex hull containing no analytic structure.

@article{AIF_1998__48_3_785_0,
     author = {Alexander, Herbert},
     title = {Hulls of subsets of the torus in ${\mathbb {C}}^2$},
     journal = {Annales de l'Institut Fourier},
     pages = {785--795},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {48},
     number = {3},
     year = {1998},
     doi = {10.5802/aif.1639},
     mrnumber = {99g:32022},
     zbl = {0910.32013},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.1639/}
}
TY  - JOUR
AU  - Alexander, Herbert
TI  - Hulls of subsets of the torus in ${\mathbb {C}}^2$
JO  - Annales de l'Institut Fourier
PY  - 1998
SP  - 785
EP  - 795
VL  - 48
IS  - 3
PB  - Association des Annales de l’institut Fourier
UR  - http://archive.numdam.org/articles/10.5802/aif.1639/
DO  - 10.5802/aif.1639
LA  - en
ID  - AIF_1998__48_3_785_0
ER  - 
%0 Journal Article
%A Alexander, Herbert
%T Hulls of subsets of the torus in ${\mathbb {C}}^2$
%J Annales de l'Institut Fourier
%D 1998
%P 785-795
%V 48
%N 3
%I Association des Annales de l’institut Fourier
%U http://archive.numdam.org/articles/10.5802/aif.1639/
%R 10.5802/aif.1639
%G en
%F AIF_1998__48_3_785_0
Alexander, Herbert. Hulls of subsets of the torus in ${\mathbb {C}}^2$. Annales de l'Institut Fourier, Tome 48 (1998) no. 3, pp. 785-795. doi : 10.5802/aif.1639. http://archive.numdam.org/articles/10.5802/aif.1639/

[A] H. Alexander, Continuing 1-dimensional analytic sets, Math. Ann., 191 (1971), 143-144. | MR | Zbl

[DS] K. Davidson and N. Salinasa, Joint quasitriangularity of essentially unitary pairs, American J. Math., 115 (1993), 861-879. | MR | Zbl

[D] J.-P. Demailly, Courants positifs extrêmaux and conjecture de Hodge, Invent. Math., 69 (1982), 347-374. | MR | Zbl

[DL] J. Duval and N. Levenberg, Large polynomial hulls with no analytic structure, to appear in Complex Analysis and Geometry, Trento, 1995. | Zbl

[DSib] J. Duval and N. Sibony, Polynomial convexity, rational convexity and currents and currents, Duke Math. J., 79 (1995), 487-519. | MR | Zbl

[FL] J.-E. Fornaess and N. Levenberg, A nonpluripolar hull with no analytic structure, to appear in Complex Analysis in Several Variables, editor T. M. Rassias. | Zbl

[Sh] B. Shiffman, On the continuation of analytic curves, Math Ann., 185 (1970), 1-12. | MR | Zbl

[Sl] Z. Slodkowski, Analytic set-valued functions and spectra, Math. Ann., 256 (1981), 363-386. | MR | Zbl

[St] K. Stein, Meromorphic mappings, l'Enseignement Math., Ser. II, 14 (1968), 29-46. | MR | Zbl

[S] G. Stolzenberg, A hull with no analytic structure, J. Math. Mech., 12 (1963), 103-112. | MR | Zbl

[W] J. Wermer, Polynomial convex hulls and analyticity, Ark. Mat., 20 (1982), 129-135. | MR | Zbl

Cité par Sources :