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平行四边形及等腰梯形的单叶性内径 被引量：3

The Inner Radius of Univalence of Parallelogram and Isosceles Trapezoid
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摘要 应用Wieren的方法研究了一类平行四边形及等腰梯形,得到了这类平行四边形及等腰梯形的单叶性内径,并证明了它们均为Nehari圆. The inner radius of some classes of parallelogram and isosceles trapezoid are investigated by the means of Wieren.The value of the inner radius are obtained and those plane domains are proved to be Nehari disk.
作者 刘新斌 杨宗信
机构地区 江西师范大学数学与信息科学学院
出处 《江西师范大学学报（自然科学版）》 CAS 北大核心 2010年第3期267-270,共4页 Journal of Jiangxi Normal University(Natural Science Edition)
基金 国家自然科学基金(10771059) 江西省自然科学基金(2007GZS0166) 江西省教育厅科研计划(GJJ09148)资助项目
关键词 SCHWARZ导数 Nehari圆 单叶性内径 Schwarzian derivative Nehari disk inner radius of univalence
分类号 O174.51 [理学—基础数学]
  • 相关文献

参考文献13

  • 1Leila Miller-Van Wieren.Univalence criteria for classes of rectangles and equiangular hexagons[J].Ann Acad Sci Fenn Math,1997,22:407-424.
  • 2Nehari Z.The Schwarzian derivative and Schlicht functions[J].Bull Amer Math Soc,1949,55:545-551.
  • 3Hille E.Remarks on a paper of zeev Nehari[J].Bull Amer Math Soc,1949,55:552-553.
  • 4Lehtinen M.On the inner radius of univalency for non-circular domains[J].Ann Acad Sci Fenn Ser A I Math,1980,5:45-47.
  • 5Ahlfors L V.Quasi-conformal reflections[J].Acta Math,1963,109:291-301.
  • 6Ahlfors L V.Lectures on quasi-conformal mappings[M].New York:Nostrand Company,1966.
  • 7Ahlfors L V.Sufficient condition for quasi-conformal extension[J].Ann of Math Studies,1974,79:23-29.
  • 8Gehring F W.Univalent functions and the Schwarzian derivative[J].Commentarii Mathematici Helvetici,1977,52:561-572.
  • 9Lehto O.Remarks on theorem about the Schwarzian derivative and Schlicht function[J].J Analyse Math,1979,36:184-190.
  • 10Calvis D.The inner radius of univalence of normal circular triangles and regular polygons[J].Complex Variables and Elliptic Equations,1985,4:295-304.

二级参考文献14

  • 1[1]Leila Miller-Van Wieren Univalence criteria for classes of rectanglesand equiangularhexagon [J],Ann. Acad. Sci. Fenn. Math.,22(1997),407--424
  • 2[2]David Calvis The inner radius of univalence of normal circular trianglesand regular polygons [J],Complex Varibles,(1985),295--304
  • 3[3]Lehtinen, M. On the inner radius of univalency for noncircular domains[J],Ann. Acad. Sci. Fenn. Ser., AI Math.,5(1980),45--47
  • 4[4]Lehto Remarks on Nehari's theorem about the Schwarzian derivativeand schlicht functions [J], J. Analyse Math., 26(1979), 180--190
  • 5[5]Ahlfors, L. V. Complex analysis [M], Second Ediction, McGraw-Hill, New York,1966
  • 6Nahari Z. The Schwarizn derivative and Schlidht functions[ J]. Bull Amer Math Soc, 1949,55:545-551.
  • 7Hill E. Remarks on a paper by Zeev Nehari[J]. Bull Amer Math Soc, 1949,55:552-553.
  • 8Lehtinen M. On the inner radius of univalency for non-circular domains[J]. Ann Acad Sci Fenn Ser A I Math, 1980,5:45-47.
  • 9Ahlfors M V. Qusiconformal reflections[J] .Acta Math, 1963, 109:291-301.
  • 10Gehring F W. Univalent functions and the Schwarz derivative[J] .Comm Math Helv, 1977, 52: 561-572.

共引文献8

同被引文献24

  • 1CHENJIXIU],WEIHANBAI.SOME GEOMETRIC PROPERTIES ON A MODE L OF UNIVERSAL TEICHMULLER SPACES[J].Chinese Annals of Mathematics,Series B,1997,18(3):309-314. 被引量：12
  • 2Ahlfors L V,Weill G.A uniqueness theorem for Beltrami equations[J] .Proc Amer Math Soc,1962,13 (6):975-978.
  • 3Ahlfors L V.Quasiconformal reflections[J] .Acta Math,1963,109(1):291-301.
  • 4Gehring F W.Characteristic properties of quasidisks[D] .Montreal:Les Presses de L' Universite de Montreal,1982.
  • 5Nehari Z.The Schwarzian derivative and schlicht functions[J] .Bull Amer Math Soc,1949,55(6):545-551.
  • 6Hille E.Remarks on a paper by Zeev Nehari[J] .Bull Amer Math Soc,1949,55 (6):552-553.
  • 7Lehtinen M.On the inner radius of univalency for non-circular domains[J] .Ann Acad Sci Fenn Ser A I Math,1980,5(1):45-47.
  • 8Lehto O.Univalent functions and teichmuller spaces[M] .New York:Springer-Varlag,1987.
  • 9Lehto O.Remarks on Neharig theorem about the Schwarzian derivative and schlicht functions[J] .Journal d' Analyse Math,1979,36 (1):184-190.
  • 10Calvis D.The inner radius of univalence of normal circular triangles and regular polygons[J] .Complex Variables,1985,4(3):295-304.

引证文献3

江西师范大学学报（自然科学版）
2010年 第3期

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