Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지

LOCAL STRUCTURE OF TRAJECTORY FOR EXTREMAL FUNCTIONS

  • Published : 1999.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

IN this note we study more about the omitted are for the extremal functions and its {{{{ {π } over {4 } }}}}-property based upon Schiffer's variational method and zBrickman-Wilken's result. we give an example other than the Koebe function which is both a support point of S and the extreme point of HS. Furthermore, we discuss the relations between the support points and the L wner chain.

Keywords

References

  1. Bull. Amer. Math. Soc. v.76 Extreme points of the set of univalent functions L. Brickman
  2. Trans. Amer. Math. Soc. v.156 Convex hulls of some classical families of univalent functions L. Brickman;T. H. MacGregor;D. R. Wilken
  3. Proc. Amer. Math. Soc. v.42 Support point of the set of univalent functions L. Brickman;D. R. Wilken
  4. Trans. Amer. Math. Soc. v.287 A method for investigating gemetric properties of support points and applications J. E. Brown
  5. Univalent functions P. Duren
  6. Complex variables: Theory and Applications Support points with maximum radial angle P. Duren;Y. Leung;M. Schiffer
  7. Translations. Math. Mono.;Amer. Math. Soc. Providence R. I. v.26 Geometric theory of functions of a complex variable G. W. Goluzin
  8. Trans. Amer. Math. Soc. v.185 Extreme points for some classes of univalent functions W. Hengartner;G. Schober
  9. Michigan Math. J. v.23 Some new properties of support points for compact families of univalent functions in the unit disk W. Hengartner;G. Schober
  10. Michigan Math. J. v.25 Extremal properties of a class of slit conformal mappings W. Kirwan;R. Pell
  11. Math. Z. v.3 Untersuchugen uber Schilichte Konforme Abbildungen des Einheitskreises K. Lowner
  12. Proc. Amer. Math. Soc. v.81 New support points of S and extreme points of HS K. Pearce
  13. Ann. Acad. Sci. Fenn. Ser. AI v.489 Linear Extremal probleme bei Schlichten Functionen A. Pfluger
  14. Proc. London. Math. Soc. v.44 A method of variation within the family of simple functions M. Schiffer
  15. Trans. Amer. Math. Soc. v.134 On the coefficient problem for univalent functions M. Schiffer