Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (5): 1142-1150.
Previous Articles Next Articles
Algebraic, Hölder and Quasisymmetric Exponents of a Homeomorphism
Cunji Yang1(
),Tao Cheng2,*(),Shanshuang Yang3()
- 1 Department of Mathematics and Computer, Dali University, Yunnan Dali 671003
2 School of Mathematical Sciences, East China Normal University, Shanghai 200241
3 Department of Mathematics, Emory University, Atlanta, GA 30322, USA
-
Received:2019-01-15Online:2020-10-26Published:2020-11-04 -
Contact:Tao Cheng E-mail:kmycj@126.com;tcheng@math.ecnu.edu.cn;syang05@emory.edu -
Supported by:the NSFC(11861005);the NSFC(11871215);the Science and Technology Commission ofShanghai Municipality(18dz2271000)
CLC Number:
- O174.5
Cite this article
Cunji Yang,Tao Cheng,Shanshuang Yang. Algebraic, Hölder and Quasisymmetric Exponents of a Homeomorphism[J].Acta mathematica scientia,Series A, 2020, 40(5): 1142-1150.
share this article
| 1 |
Cheng T , Yang S . Dilatations and exponents of quasisymmetric homeomorphisms. Ann Acad Sci Fenn Math, 2016, 41, 287- 304
doi: 10.5186/aasfm.2016.4122 |
| 2 |
Anderson J , Hinkkanen A . Quadrilaterals and extremal quasiconformal extensions. Comment Math Helv, 1995, 70, 455- 474
doi: 10.1007/BF02566018 |
| 3 |
Chen J , Chen Z . A remark on "an approximation condition and extremal quasiconformal extension". Chinese Science Bulletin, 1997, 42, 1765- 1767
doi: 10.1007/BF02882637 |
| 4 |
Shen Y . A counterexample theorem in quasiconformal mapping theory. Sci China Ser A, 2000, 43, 929- 936
doi: 10.1007/BF02879798 |
| 5 |
Wu S . Moduli of quadrilaterals and extremal quasiconformal extensions of quasisymmetric functions. Comment Math Helv, 1997, 72, 593- 604
doi: 10.1007/s000140050036 |
| 6 |
Yang S . On dilatations and substantial boundary points of homeomorphisms of Jordan curves. Results Math, 1997, 31, 180- 188
doi: 10.1007/BF03322160 |
| 7 |
Cheng T , Yang S . Decomposition of extremal length and a proof of Shen's conjecture on QED constant and boundary dilatation. Math Z, 2014, 278, 1195- 1211
doi: 10.1007/s00209-014-1353-z |
| 8 |
Cheng T , Yang S . Extremal function for capacity and estimates of QED constants in  doi: 10.1016/j.aim.2016.10.039 |
| 9 | Gehring F W, Martio O. Quasiextremal distance domains and extension of quasiconformal mappings. J d'Analyse Math, 1985, 45: 181-206 |
| 10 |
Shen Y . Conformal invariants of QED domains. Tohoku Math J, 2004, 56, 445- 466
doi: 10.2748/tmj/1113246678 |
| 11 |
Shen Y . Various constants associated with quasidisks and quasisymmetric homeomorphisms. Publications de L'Institut Mathematique, 2004, 75 (89): 95- 107
doi: 10.2298/PIM0475095Y |
| 12 |
Yang S . QED domains and NED sets in  |
| 13 |
Beurling A , Ahlfors L V . The boundary correspondence under quasiconformal mappings. Acta Math, 1956, 96, 125- 142
doi: 10.1007/BF02392360 |
| 14 | Heinonen J . Lectures on Analysis on Metric Spaces. New York:Spring-Verlag, 2001 |
| 15 |
Tukia P , Väisälä J . Quasisymmetric embeddings of metric spaces. Ann Acad Sci Fenn Math, 1980, 5, 97- 114
doi: 10.5186/aasfm.1980.0531 |
| 16 | Ahlfors L V . Lectures on Quasiconformal Mappings. Toronto:D Van Nostrand Co Inc, 1966 |
| 17 | Lehto O . Univalent Functions and Teichmüller Spaces. New York:Springer-Verlag, 1986 |
| 18 | Ahlfors L V . Conformal Invariants. New York:McGraw-Hill, 1973 |
| [1] | Qi Yi, Shi Qingtian. Estimations of Convexity Radius and the Norm of Pre-Schwarz Derivative for Close to Convex Harmonic Mappings [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1057-1066. |
| [2] | ZHU Jian-Feng, HUANG Xin-Zhong. The Univalent Radius of Harmonic Mappings Under Complex-Operator [J]. Acta mathematica scientia,Series A, 2014, 34(1): 171-178. |
| [3] | HUANG Hua-Ying. Teichm\"uller Mappings and the Mappings by Heights for Guadratic Differentials [J]. Acta mathematica scientia,Series A, 2013, 33(6): 1062-1067. |
| [4] | CHU Yu-Meng, WANG Gen-Di, ZHANG Xiao-Hui. Double-disk Property of Curves and Quasiconformal Mappings [J]. Acta mathematica scientia,Series A, 2009, 29(2): 239-244. |
| [5] | Liao Maoxin; Chu Yuming; Li Xianyi. Uniform Domain and Max-min Inequality Property [J]. Acta mathematica scientia,Series A, 2009, 29(1): 121-126. |
| [6] |
Zheng Ningguo; Chu Yuming.
The Holder Continuity of Quasiconformal Mappings in Bounded Convex Domains [J]. Acta mathematica scientia,Series A, 2008, 28(3): 565-569. |
| [7] | Liao Maoxin; Chu Yuming. Quasiconformal Mappings and Hausdorff Dimension [J]. Acta mathematica scientia,Series A, 2008, 28(1): 183-187. |
| [8] |
Chu Yuming;Zhang Xiaohui\quad ;Wang Gendi.
The Supremum of Lp -integrability Exponent on Quasiconformal Mappings [J]. Acta mathematica scientia,Series A, 2007, 27(6): 1021-1024. |
| [9] |
Qi Yi ;Wu Yan.
The Maximal Dilatation and Boundary Dilatation of Quasi-symmetric Mapping [J]. Acta mathematica scientia,Series A, 2007, 27(5): 839-844. |
| [10] | Chu Yuming;Huang Manzi. A Necessary and Sufficient Condition for Quasiconformal Mappings [J]. Acta mathematica scientia,Series A, 2007, 27(5): 949-954. |
| [11] | Chu Yuming. The Distortion of Cross Ratio and Poincare Metric under Plane Quasiconformal Mappings [J]. Acta mathematica scientia,Series A, 2007, 27(4): 748-752. |
| [12] | Chen Zhiguo. Boundary Behavior of μ(z)-homeomorphisms [J]. Acta mathematica scientia,Series A, 2007, 27(1): 67-76. |
| [13] | Wu Zhaojun, Sun Daochun. On the Borel Direction of Largest Type of Quasimeromorphic Mappings [J]. Acta mathematica scientia,Series A, 2006, 26(1): 15-020. |
| Viewed | ||||||||||||||||||||||||||||||||||||||||||||||
|
Full text 115
|
|
|||||||||||||||||||||||||||||||||||||||||||||
|
Abstract 109
|
|
|||||||||||||||||||||||||||||||||||||||||||||
Cited |
|
|||||||||||||||||||||||||||||||||||||||||||||
| Shared | ||||||||||||||||||||||||||||||||||||||||||||||
| Discussed | ||||||||||||||||||||||||||||||||||||||||||||||
|