On the Estimates of Hyperbolic Area Distortion of Quasiconformal Mappings

Chinese Quarterly Journal of Mathematics ›› 2007, Vol. 22 ›› Issue (1): 137-142.

On the Estimates of Hyperbolic Area Distortion of Quasiconformal Mappings

Department of Mathematics,Huaqiao University,Quanzhou 362021,China

Received:2004-02-17 Online:2007-03-30 Published:2023-11-16
About author:CHEN Xing-di(1976-),male,native of Quanzhou,Fujian,a lecturer of Huaqiao University, M.S.D.,engages in complex analysis theory;HUANG Xin-zhong(1957-),male,native of Quanzhou,Fujian,a professor of Huaqiao University,Ph.D.,engages in complex analysis theory.
Supported by:
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)；

Abstract

Abstract: 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.

Key words: hyperbolic area, quasiconformal mapping, explodable set, distortion estimate ,

CLC Number:

O174.55

CHEN Xing-di, HUANG Xin-zhong. On the Estimates of Hyperbolic Area Distortion of Quasiconformal Mappings[J]. Chinese Quarterly Journal of Mathematics, 2007, 22(1): 137-142.

[1]	ZOU Mian-lu, LI Qiang. Some New Regularity Criteria for the 3D Boussinesq Equations in Homogeneous Besov Spaces [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 73-81.
[2]	LIU Gong-wei, YANG Kun. Finite Time Blow-Up and Global Existence for Degenerate Parabolic Equations at High Initial Energy [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 97-110.
[3]	TANG Zhong-hua, FANG Shao-mei. Implicit Finite Difference Method for Time-Space Caputo-Riesz Fractional Diffusion Equation with Fractional Robin Boundary Conditions [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 18-30.
[4]	LI Hong-jun. Hopf-Rinow Theorem on Convex Complex Finsler Manifolds [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 31-45.
[5]	PAN Jia-hui, FANG Shao-mei. Initial Boundary Value Problem for Pseudo-Parabolic p-Laplacian Type Equation with Logarithmic Nonlinearity [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(4): 360-369.
[6]	SUN Xiao-lei. Competitive Equilibrium of Central Bank Digital Currency and Private Cryptocurrency: A Perspective of Regulatory [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(4): 415-423.
[7]	YANG Yi-song. Some Applications of Surface Curvatures in Theoretical Physics [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 221-253.
[8]	GUAN Daniel. Some Applications of Group Actions in Complex Geometry [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 254-275.
[9]	QIN Yu-ming, CHEN Jia-le, JIANG Hui-te. A New Existence Theorem for Global Attractors and its Application to a Non-Classical Diffusion Equation [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 276-289.
[10]	WANG Shu, SUN Rui. Global Well-Posedness of the Initial-Boundary Value Problem on Incompressible MHD-Boussinesq Equations with Nonlinear Boundary Conditions [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 290-310.
[11]	XU Xiao-meng. On the Stokes Phenomenon and Representation Theory of Quantum Groups [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 311-330.
[12]	LIU Liang, WANG Ya-qiang. New Criteria for Nonsingular H-Tensors [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(2): 123-133.
[13]	MA Teng. Multilinear Calderón-Zygmund Operators with Kernels of#br# Dini Type and Commutators in Variable Exponent#br# Central Morrey Spaces [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(2): 184-195.
[14]	DONG Chang-zhou, LI Hao-xue. The Least Squares {P,Q,k+1}-Reflexive Solution to a Matrix Equation [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(2): 210-220.
[15]	REN Shi-quan, WANG Chong. Weighted Analytic Torsion for Weighted Digraphs [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(1): 30-49.

On the Estimates of Hyperbolic Area Distortion of Quasiconformal Mappings

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments