The simple-zero theorem for support points in Σ

Leung, Y. J.; Schober, G.

doi:10.1090/S0002-9939-1989-0948155-X

The simple-zero theorem for support points in $\Sigma$
HTML articles powered by AMS MathViewer

by Y. J. Leung and G. Schober PDF

Proc. Amer. Math. Soc. 105 (1989), 603-608 Request permission

Abstract:

The purpose of this article is to confirm a simple-zero conjecture raised by the second author for support points in $\Sigma$. The conjecture implies that the omitted arcs of an extremal function in $\Sigma$ for a linear problem can branch out in, at most, three equiangular directions at a time.

References

Yusuf Abu-Muhanna and Y. J. Leung, On analytic slit mappings in the class $\Sigma$, Proc. Amer. Math. Soc. 99 (1987), no. 1, 44–48. MR 866427, DOI 10.1090/S0002-9939-1987-0866427-2
A. Chang, M. M. Schiffer, and G. Schober, On the second variation for univalent functions, J. Analyse Math. 40 (1981), 203–238 (1982). MR 659792, DOI 10.1007/BF02790163
William E. Kirwan and Glenn Schober, New inequalities from old ones, Math. Z. 180 (1982), no. 1, 19–40. MR 656220, DOI 10.1007/BF01214997
Y. J. Leung and G. Schober, Low order coefficient estimates in the class $\Sigma$, Ann. Acad. Sci. Fenn. Ser. A I Math. 11 (1986), no. 1, 39–61. MR 826348, DOI 10.5186/aasfm.1986.1111
Y. J. Leung and G. Schober, On the structure of support points in the class $\Sigma$, J. Analyse Math. 46 (1986), 176–193. MR 861698, DOI 10.1007/BF02796584
Christian Pommerenke, Univalent functions, Studia Mathematica/Mathematische Lehrbücher, Band XXV, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen. MR 0507768
Glenn Schober, Univalent functions—selected topics, Lecture Notes in Mathematics, Vol. 478, Springer-Verlag, Berlin-New York, 1975. MR 0507770, DOI 10.1007/BFb0077279
Glenn Schober, Some conjectures for the class $\Sigma$, Topics in complex analysis (Fairfield, Conn., 1983) Contemp. Math., vol. 38, Amer. Math. Soc., Providence, RI, 1985, pp. 13–21. MR 789441, DOI 10.1090/conm/038/02
Kurt Strebel, Quadratic differentials, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 5, Springer-Verlag, Berlin, 1984. MR 743423, DOI 10.1007/978-3-662-02414-0