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On the Estimates of Hyperbolic Area Distortion of Quasiconformal Mappings 被引量：1

On the Estimates of Hyperbolic Area Distortion of Quasiconformal Mappings
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摘要 The distortion property of hyperbolic area of planar quasiconformal mappings is studied in this paper. In the case of radial quasiconformal mappings and angular deformed quasiconformal mappings their hyperbolic area distortions are estimated quite sharply. The result can be applied to judge whether the hyperbolic area of a planar subset is explodable.
作者 CHEN Xing-di HUANG Xin-zhong
机构地区 Department of Mathematics
出处 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第1期137-142,共6页 数学季刊（英文版）
基金 Supported by the Natural Science Foundation of Huaqiao University(02HZR12) Supported by the Natural Science Foundation of Overseas Chinese Affairs Office under the State Council(01QZR01)
关键词 hyperbolic area quasiconformal mapping explodable set distortion estimate 拟共形映射 双曲线区 失真 估计
分类号 O174.55 [理学—基础数学]
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参考文献7

  • 1GEHRING F W. REICH E. Area distortion under quasiconformal mappings[J]. Ann Acad Sci Fenn Ser AI Math, 1996, 388: 1-14.
  • 2ASTALA K. Area distortion of quasiconformal mappings[J]. Acta Math, 1994, 173(1): 37-60.
  • 3EREMENKO A. HAMILTON D H. On the area distortion by quasiconformal mappings[J]. Proc Amer Math Soc, 1995, 123(9): 2793-2797.
  • 4PORTER R M. RESENDIS L F. Quasiconformally explodable sets[J]. Complex Variables, 1998, 36(4): 379-392.
  • 5CHEN Xing-di, HUANG Xin-zhong. Explodable sets of quasiconformal mapping[J]. Journal of Huaqiao Univ(Natural Science), 2001, 22(2): 111-116.
  • 6REICH E, WALCAZK H. On the behavior of quasiconformal mappings at a point[J]. Trans Amer Math Soc, 1965, 117: 338-351.
  • 7GUTLYANSKII V Y. SUGAWA T. On Lipschitz continuity of quasiconformal mappings[J]. Report Univ Jyvaskyla, 2001, 83: 91-108.

同被引文献13

  • 1AHLFORS L V.Complex analysis[M].3rd ed.New York:McGraw-Hill Book Company,1979.
  • 2LEWY H.On the non-vanishing of the Jacobian in certain one to one mapings[J].Bull Amer Math Soc,1936,42(10):689-692.
  • 3PARTYKA D,SAKAN K I.On an asymptotically sharp variant of Heinz's inequality[J].Ann Acad Sci Fenn Ser AI,2005,30(1):167-182.
  • 4ASTALA K.Area distortion of quasiconformal mappings[J].Acta Math,1994,173(1):37-60.
  • 5CHEN Xing-di,FANG Ainong.Harmonic Teichmüller mappings[J].Proc Japan Acad Ser (A):Math Sci,2006,82(7):101-105.
  • 6KELINGOS J A.Distortion of hyperbolic area under quasiconformal mappings[J].Duke Math J,1974,41(1):127-139.
  • 7PORTER R M,RESNDIS L F.Quasiconformally explodable sets[J].Complex Variables,1998,36(4):379-392.
  • 8KALAJ D,PAVLOVIC M.Boundary correspondence under quasiconformal harmonic diffeomorphisms of a half-plane[J].Ann Acad Sci Fen Math,2005,30(1):159-165.
  • 9AHLFORS L V.Conformal invariants:Topics in geometric function theory[M].New York:McGraw-Hill Book Company,1973.
  • 10WAN T.Constant mean curvature surface,harmonic maps and universal Teichmüller space[J].J Differential Geom,1992,35(3):643-657.

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Chinese Quarterly Journal of Mathematics
2007年 第1期

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