A disc-hull in 𝐶²

A disc-hull in $\textbf {C}^ 2$
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by H. Alexander

Proc. Amer. Math. Soc. 120 (1994), 1207-1209

DOI: https://doi.org/10.1090/S0002-9939-1994-1179585-3

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We construct a compact set in ${{\mathbf {C}}^2}$ whose disc-hull is a proper dense subset of its polynomial hull.

References

Patrick Ahern and Walter Rudin, Hulls of $3$-spheres in $\textbf {C}^3$, The Madison Symposium on Complex Analysis (Madison, WI, 1991) Contemp. Math., vol. 137, Amer. Math. Soc., Providence, RI, 1992, pp. 1–27. MR 1190966, DOI 10.1090/conm/137/1190966
H. Alexander, B. A. Taylor, and J. L. Ullman, Areas of projections of analytic sets, Invent. Math. 16 (1972), 335–341. MR 302935, DOI 10.1007/BF01425717
Errett Bishop, Holomorphic completions, analytic continuation, and the interpolation of semi-norms, Ann. of Math. (2) 78 (1963), 468–500. MR 155016, DOI 10.2307/1970537
Gabriel Stolzenberg, A hull with no analytic structure, J. Math. Mech. 12 (1963), 103–111. MR 0143061
J. Wermer, Polynomially convex hulls and analyticity, Ark. Mat. 20 (1982), no. 1, 129–135. MR 660131, DOI 10.1007/BF02390504