본문 바로가기
KERD
논문KCI 등재

A criterion for vertex extremal length parabolic graphs and its application

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

We give a criterion for vertex extremal length parabolicity of locally finite planar graphs, and use it to show that a disk triangulation graph is circle packing parabolic if and only if its immediate finer graphs are circle packing parabolic.

Abstract

We give a criterion for vertex extremal length parabolicity of locally finite planar graphs, and use it to show that a disk triangulation graph is circle packing parabolic if and only if its immediate finer graphs are circle packing parabolic.

참고문헌 (12)

  1. L. Ahlfors, "Conformal Invariants" (1973), McGraw-Hill
  2. J.W. Cannon, "The combinatorial Riemann mapping theorem", Acta Math., 173, pp.155~234 (1994)
  3. R.J. Duffm, "The extremal length of a network", J. Math. Anal. Appl., 5, pp.200~215 (1962)
  4. Z. He, "Fixed points, Koebe uniformization and circle packings", Ann. of Math., 137(2), pp.369~406 (1993)
  5. Z. He, "Hyperbolic and parabolic packings", Discrete Comput. Geom., 14(2), pp.123~149 (1995)
  6. S. Merenkov, "Classical and cp-types of surfaces of class S, in preper-ation", ~
  7. R. Nevanlinna, "Analytic Functions" (1970), Springer-Verlag
  8. B. Rodin, "The convergence of circle packings to the Riemann mapping", J. Differential Geom., 26(2), pp.349~360 (1987)
  9. O. Schramm, "Transboundary extremal length", J. Anal. Math., 66, pp.307~329 (1995)
  10. K. Stephenson, "Circle packing: a mathematical tale", Notices Amer. Math. Soc., 50(11), pp.1376~1388 (2003)
  11. K. Stephenson, "Introduction to circle packing; the theory of discrete analytic functions" (2005), Cambridge University Press
  12. W.P. Thurston, "The finite Riemann mapping theorem", Unpublished talk given at the International Symposium in Celebration of the Proof of the Bieberbach Conjecture (1985), Purdue University

관련 논문AI추천

이 간행물의 다른 논문 (12건)