On an example of Ahern and Rudin
HTML articles powered by AMS MathViewer
- by John T. Anderson
- Proc. Amer. Math. Soc. 116 (1992), 695-699
- DOI: https://doi.org/10.1090/S0002-9939-1992-1129870-4
- PDF | Request permission
Abstract:
We show that the polynomial hull of a certain totally real three-sphere in ${\mathbb {C}^3}$ constructed by Ahern and Rudin is the union of a two-parameter family of analytic disks.References
- Patrick Ahern and Walter Rudin, Totally real embeddings of $S^3$ in $\textbf {C}^3$, Proc. Amer. Math. Soc. 94 (1985), no. 3, 460–462. MR 787894, DOI 10.1090/S0002-9939-1985-0787894-7 —, Hulls of $3$-spheres in ${\mathbb {C}^3}$, preprint, 1991.
- H. Alexander, A note on polynomial hulls, Proc. Amer. Math. Soc. 33 (1972), 389–391. MR 294689, DOI 10.1090/S0002-9939-1972-0294689-0
- H. Alexander, Polynomial hulls of graphs, Pacific J. Math. 147 (1991), no. 2, 201–212. MR 1084704
- John T. Anderson, Polynomial hulls of sets invariant under an action of the special unitary group, Canad. J. Math. 40 (1988), no. 5, 1256–1271. MR 973520, DOI 10.4153/CJM-1988-054-9
- Errett Bishop, Differentiable manifolds in complex Euclidean space, Duke Math. J. 32 (1965), 1–21. MR 200476
- Franc Forstnerič, A totally real three-sphere in $\textbf {C}^3$ bounding a family of analytic disks, Proc. Amer. Math. Soc. 108 (1990), no. 4, 887–892. MR 1038758, DOI 10.1090/S0002-9939-1990-1038758-7
- T. W. Gamelin, Hartogs series, Hartogs functions and Jensen measures, Spaces of analytic functions (Sem. Functional Anal. and Function Theory, Kristiansand, 1975) Lecture Notes in Math., Vol. 512, Springer, Berlin, 1976, pp. 69–83. MR 0486632
- Mikhael Gromov, Partial differential relations, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 9, Springer-Verlag, Berlin, 1986. MR 864505, DOI 10.1007/978-3-662-02267-2
- John Wermer, Subharmonicity and hulls, Pacific J. Math. 58 (1975), no. 1, 283–290. MR 393567
Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 695-699
- MSC: Primary 32E20
- DOI: https://doi.org/10.1090/S0002-9939-1992-1129870-4
- MathSciNet review: 1129870