We construct a non-polynomially convex compact subset of the unit torus in with polynomially convex hull containing no analytic structure.
Nous donnons une construction d’un compact non-polynomialement convexe dans le tore standard de tel que son enveloppe polynomiale soit sans structure analytique.
@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},
year = {1998},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {48},
number = {3},
doi = {10.5802/aif.1639},
zbl = {0910.32013},
mrnumber = {99g:32022},
language = {en},
url = {https://aif.centre-mersenne.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 - https://aif.centre-mersenne.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 https://aif.centre-mersenne.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, Volume 48 (1998) no. 3, pp. 785-795. doi: 10.5802/aif.1639
[A] , Continuing 1-dimensional analytic sets, Math. Ann., 191 (1971), 143-144. | MR | Zbl
[DS] and , Joint quasitriangularity of essentially unitary pairs, American J. Math., 115 (1993), 861-879. | Zbl | MR
[D] , Courants positifs extrêmaux and conjecture de Hodge, Invent. Math., 69 (1982), 347-374. | Zbl | MR
[DL] and , Large polynomial hulls with no analytic structure, to appear in Complex Analysis and Geometry, Trento, 1995. | Zbl
[DSib] and , Polynomial convexity, rational convexity and currents and currents, Duke Math. J., 79 (1995), 487-519. | Zbl | MR
[FL] and , A nonpluripolar hull with no analytic structure, to appear in Complex Analysis in Several Variables, editor T. M. Rassias. | Zbl
[Sh] , On the continuation of analytic curves, Math Ann., 185 (1970), 1-12. | Zbl | MR
[Sl] , Analytic set-valued functions and spectra, Math. Ann., 256 (1981), 363-386. | Zbl | MR
[St] , Meromorphic mappings, l'Enseignement Math., Ser. II, 14 (1968), 29-46. | Zbl | MR
[S] , A hull with no analytic structure, J. Math. Mech., 12 (1963), 103-112. | Zbl | MR
[W] , Polynomial convex hulls and analyticity, Ark. Mat., 20 (1982), 129-135. | Zbl | MR
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