Some new results on planar harmonic mappings 被引量：2

Some new results on planar harmonic mappings

导出

摘要 This survey paper contains some new results on the Landau theorem, Bloch theorem and Schwarz-Pick lemma for planar harmonic mappings. This survey paper contains some new results on the Landau theorem, Bloch theorem and Schwarz-Pick lemma for planar harmonic mappings.

作者 CHEN HuaiHui Department of Mathematics, Nanjing Normal University, Nanjing 210097, China

出处《Science China Mathematics》 SCIE 2010年第3期597-604,共8页 中国科学：数学（英文版）

基金 supported by National Natural Science Foundation of China(Grant No. 10671093)

关键词 harmonic mapping LANDAU THEOREM BLOCH constant Schwarz-Pick LEMMA quasi-regularity harmonic mapping Landau theorem Bloch constant Schwarz-Pick lemma quasi-regularity

分类号 O174.3 [理学—基础数学]

引文网络
相关文献

参考文献2

1LIU MingSheng School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China.Estimates on Bloch constants for planar harmonic mappings[J].Science China Mathematics,2009,52(1):87-93. 被引量：16
2CHEN HuaiHui.The Schwarz-Pick lemma for planar harmonic mappings[J].Science China Mathematics,2011,54(6):1101-1118. 被引量：9

二级参考文献18

1LIU MingSheng School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China.Estimates on Bloch constants for planar harmonic mappings[J].Science China Mathematics,2009,52(1):87-93. 被引量：16
2Huaihui Chen,Chengji Xiong.Julia’s lemma and bloch constants[J]. Science in China Series A: Mathematics . 2003 (3)
3DorM,Nowak M.Landau’s theorem for planar harmonic mappings. Comput Methods Funct Theory . 2000
4Grigoryan A.Landau and Bloch theorems for harmonic mappings. Complex Variables Theory and Application . 2006
5Huang X Z.Estimates on Bloch constants for planar harmonic mappings. Journal of Mathematical Analysis and Applications . 2007
6Chen H H,Xiong C J.Julia’s lemma and Bloch constants. Sci China Ser A-Math . 2003
7Chen H H.On the Bloch constant. Approximation, Complex Analysis, and Potential Theory . 2001
8Lewy,H.On the non-vanishing of the Jacobian in certain one-to-one mappings. Bulletin of the American Mathematical Society . 1936
9CHEN H,,GAUTHIER P M,HENGARTNER W.Bloch constants for planar harmonic mappings. Poc AmerMath Soc . 2000
10Graham,I.,Kohr,G. Geometric Function Theory in One and Higher Dimensions . 2003

共引文献23

1刘名生,刘志文,朱玉灿.某类双调和映射的Landau型定理[J].数学学报（中文版）,2011,54(1):69-80. 被引量：4
2夏小青,黄心中.一类双调和映照的单叶半径估计[J].华侨大学学报（自然科学版）,2011,32(2):218-221. 被引量：5
3CHEN HuaiHui.The Schwarz-Pick lemma for planar harmonic mappings[J].Science China Mathematics,2011,54(6):1101-1118. 被引量：9
4黄心中,傅冬绵.平面复值调和映照研究的一些新进展[J].漳州师范学院学报（自然科学版）,2011,24(4):1-10.
5李东征,陈行堤.调和映照的Bloch常数[J].华侨大学学报（自然科学版）,2012,33(1):103-106. 被引量：2
6CHEN HuaiHui.The Schwarz-Pick lemma and Julia lemma for real planar harmonic mappings[J].Science China Mathematics,2013,56(11):2327-2334. 被引量：4
7陈少林,PONNUSAMY Saminathan,王仙桃.多重调和映射的等周型和Fejer-Riesz型不等式[J].中国科学：数学,2014,44(2):127-138.
8王智刚,石磊,蒋月评.沿着某个方向凸的调和单叶映射的构造[J].中国科学：数学,2014,44(2):139-150.
9朱剑峰,黄心中.复微分算子下调和映照的单叶半径[J].数学物理学报（A辑）,2014,34(1):171-178. 被引量：1
10谢志春,李东征.积分算子下调和映照的单叶半径估计[J].数学的实践与认识,2019,49(2):273-278. 被引量：4

同被引文献19

1Liulan Li,Saminathan Ponnusamy.Solution to an open problem on convolutions of harmonic mappings[J].Complex Variables and Elliptic Equations.2013(12)
2Zhi-Hong Liu,Ying-Chun Li,Irena Lasiecka.The Properties of a New Subclass of Harmonic Univalent Mappings[J].Abstract and Applied Analysis.2013
3Shaolin Chen,Saminathan Ponnusamy,Xiantao Wang.Covering and distortion theorems for planar harmonic univalent mappings[J].Archiv der Mathematik.2013(3)
4Zhi-Gang Wang,Zhi-Hong Liu,Ying-Chun Li.On the linear combinations of harmonic univalent mappings[J].Journal of Mathematical Analysis and Applications.2012
5Michael Dorff,Maria Nowak,Magdalena Wo?oszkiewicz.Convolutions of harmonic convex mappings[J].Complex Variables and Elliptic Equations.2012(5)
6Huaihui Chen,Paul M. Gauthier.The Landau theorem and Bloch theorem for planar harmonic and pluriharmonic mappings[J].Proceedings of the American Mathematical Society.2010(2)
7Michael Dorff.Convolutions of planar harmonic convex mappings[J].Complex Variables and Elliptic Equations.2001(3)
8St. Ruscheweyh,T. Sheil-Small.Hadamard products of Schlicht functions and the Pólya-Schoenberg conjecture[J].Commentarii Mathematici Helvetici.1973(1)
9Selden Y. Trimble.The convex sum of convex functions[J].Mathematische Zeitschrift.1969(2)
10J. Clunie,T. Sheil-Small.Harmonic univalent functions[].Annales Academiae Scientiarum Fennicae Series A Mathematica.1984

引证文献2

1王智刚,石磊,蒋月评.沿着某个方向凸的调和单叶映射的构造[J].中国科学：数学,2014,44(2):139-150.
2漆毅,石擎天.一类近于凸调和映照的凸像半径与Pre-Schwarz导数的估计[J].数学物理学报（A辑）,2016,36(6):1057-1066. 被引量：5

二级引证文献5

1谢志春,李东征.某类Nehari函数族的边界性质[J].厦门理工学院学报,2020,28(1):85-88.
2谢志春,李东征.Nehari函数族的偏差性质与拟共形延拓[J].数学的实践与认识,2020,50(8):229-233.
3谢志春,李东征.平面调和映照的凸半径[J].数学的实践与认识,2020,50(20):208-212.
4Zhenlian LIN,Qingtian SHI.PARAMETRIC REPRESENTATIONS OF QUASICONFORMAL MAPPINGS[J].Acta Mathematica Scientia,2020,40(6):1874-1882.
5谢志春,吴丽娟,李东征.调和函数类的卷积的凸半径估计[J].数学的实践与认识,2023,53(5):226-235.

1Robust Gene Dys-Regulation in Alzheimer's Brains[J].Bulletin of the Chinese Academy of Sciences,2014,28(4):310-310.
2孙道椿,杨乐.Interation of quasi-rational mapping[J].Progress in Natural Science:Materials International,2001,11(1):18-27.
3DAI ShaoYu1,2,CHEN HuaiHui1 & PAN YiFei3,4 1Department of Mathematics,Nanjing Normal University,Nanjing 210097,China,2Department of General Study Program,Jinling Institute of Technology,Nanjing 211169,China,3School of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330022,China,4Department of Mathematical Sciences,Indiana University-Purdue University Fort Wayne,Fort Wayne,IN 46805-1499,USA.The high order Schwarz-Pick lemma on complex Hilbert balls[J].Science China Mathematics,2010,53(10):2649-2656. 被引量：7
4高洪俊,郭柏灵.Number of determining nodes for generalized Ginzburg-Landau equation[J].Progress in Natural Science:Materials International,1996,6(1):104-106.
5LIU Yang 1,& CHEN ZhiHua 2 1 Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China,2 Department of Mathematics,Tongji University,Shanghai 200092,China.Schwarz-Pick estimates for positive real part holomorphic functions on unit ball and polydisc[J].Science China Mathematics,2010,53(4):1017-1024. 被引量：3
6庞学诚.ON NORMAL CRITERION OF MEROMORPHIC FUNCTIONS[J].Science China Mathematics,1990,33(5):521-527. 被引量：22
7“2012对我来说像做梦一样”[J].电子竞技,2013(5):19-19.
8施武杰,毕建行.A CHARACTERIZATION OF SUZUKI-REE GROUPS[J].Science China Mathematics,1991,34(1):14-19. 被引量：14
9麦结华.ORIENTATION-REVERSING 2-PERIODIC SELF-HOMEOMORPHISMS OF ORIENTABLE CLOSED SURFACES[J].Chinese Science Bulletin,1992,37(8):627-631.
10马天水,李海英.从广义加权Bloch空间到Bloch-型空间的积分型算子[J].河南师范大学学报（自然科学版）,2011,39(3):10-12. 被引量：1

Science China Mathematics

2010年第3期

浏览历史

内容加载中请稍等...