Polynomially convex hulls of graphs on the sphere

Jimbo, Toshiya; Sakai, Akira

doi:10.1090/S0002-9939-99-04922-9

Polynomially convex hulls of graphs on the sphere
HTML articles powered by AMS MathViewer

by Toshiya Jimbo and Akira Sakai PDF

Proc. Amer. Math. Soc. 127 (1999), 2697-2702 Request permission

Abstract:

Let $\Sigma$ be the graph of a continuous map of the unit sphere of $\mathbb C^n$ into $\mathbb C^m$, and $h(\Sigma )$ the polynomially convex hull of $\Sigma$. Several examples of $h(\Sigma )$ for $n=m>1$ are given, which have different properties from the known ones for $n>m$.

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, Polynomial hulls of graphs, Pacific J. Math. 147 (1991), no. 2, 201–212. MR 1084704, DOI 10.2140/pjm.1991.147.201
John T. Anderson, On an example of Ahern and Rudin, Proc. Amer. Math. Soc. 116 (1992), no. 3, 695–699. MR 1129870, DOI 10.1090/S0002-9939-1992-1129870-4
Herbert Alexander and John Wermer, Polynomial hulls with convex fibers, Math. Ann. 271 (1985), no. 1, 99–109. MR 779607, DOI 10.1007/BF01455798
P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14
Akira Sakai, Uniform approximation in several complex variables, Osaka Math. J. 15 (1978), no. 3, 589–611. MR 510498
Sam Perlis, Maximal orders in rational cyclic algebras of composite degree, Trans. Amer. Math. Soc. 46 (1939), 82–96. MR 15, DOI 10.1090/S0002-9947-1939-0000015-X