Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

A GEOMETRIC APPROACH TO TWO-POINT COMPARISONS FOR HYPERBOLIC AND EUCLIDEAN GEOMETRY

  • Kim, Seong-A. (Department of mathematics Woosuk University) ;
  • Minda, David (Department of Mathematical Sciences University of Cincinnati)
  • Published : 1999.11.01
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Abstract

Two-point comparison theorems between hyperbolic and euclidean geometry for convex regions in the complex plane are known([5], [6]). We give new geometric proofs of sharp two-point comparison theorems for convex regions.

Keywords

References

  1. Comment. Math. Helv. v.53 Ein Verzerrungssatz fur schlichte Funktionen C. Blatter
  2. Israel J. Math. v.70 Hyperbolic metric, curvature of geodesics and hyperbolic discs in hyperbolic plane domains R. Harmelin
  3. Japanese J. Math v.23 On convex hyperbolic regions S. Kim
  4. J. Analysis v.1 The hyperbolic and quacihyperbolic metrics in convex regions S. Kim;D. Minda
  5. Pacifc J. Math. v.163 Two-point distortion theorems for univalent functions
  6. Complex Variables Theory Appl v.33 Two-point distortion theorems for strongly close-to-convex functions W. Ma;D. Minda
  7. J. Comp. Appl. Math. Two-point distortion for univalent functions
  8. Two-point comparisons between hyperbolic and euclidean geometry on plane regions F. Maitani;W. Ma;D. Minda
  9. J. Analysis Math. v.49 Applications of hyperbolic convexity to euclidean and spherical convexity D. Minda
  10. Rocky Mtn. J. Math. v.12 Univalence criteria and the hyperbolic metric D. Minda;D. Wright