Area distortion under the Beurling-Ahlfors extension of monomials
Keywords:
Hyperbolic area, quasiconformal mapping, Beurling-Ahlfors extensionAbstract
Area distortion under the Beurling-Ahlfors extension of monomials.
References
L. V. Ahlfors, Lectures on Quasiconformal Mappings, Van Nostrand, 1966.
K. Astala, Area distortion of quasiconformal mappings, Acta Math. 173 (1994).
J. Anderson, Hyperbolic Geometry, 1–230, Springer, London 2003.
A. Beardon, The Geometry of Discrete Groups, 1–338, Springer, New York, 1983.
A. Beurling, L.V. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 25–142.
M. Chen, X. Chen, (K,K0)-quasiconformal harmonic mappings of the upper half plane onto itself, Annales Academic Scientiarum Fennicae, Mathematica, 265–276, 2012.
F. Dongmian, H. Xinzhong, Harmonic K-Quasiconformal mappings from the unit disk onto half planes, Bulletin of the Malaysian Mathematical Sciences Society 39, Issue 1 (2016), 339–347.
F. Gehring, E. Reich, Area distortion under quasiconformal mappings, Annales Academic Scientiarum Fennicae, Mathematica AI 388 (1966), 1–14.
A. Hernández-Montes, L.F. Reséndis O.,Hyperbolic area distortion under quasiconformal mappings, J. Inequal. Appl. (2017) 2017: 211. https://doi.org/10.1186/s13660-017-1481-1
O. Lehto, Univalent Functions and Teichmüller theory, Springer-Verlarg, 1986.
O. Lehto, K. I. Virtanen, Quasiconformal Mappings in the Plane, Springer-Verlarg, 1973.
M. Kanezevic, M. Mateljević, On the quasi-isometries of harmonic quasiconformal mappings, J. Math. Ana. Appl., 404–413, 2007.
D. Kalaj, M. Maltejević, Quasiconformal harmonic mappings and generalizations, International workshop on harmonic and quasiconformal mappings 18 (2010), 239–260.
M. Mateljevic, Distortion of harmonic functions and harmonic quasiconformal quasiisometry J. Revue Roumaine des Mathematiques Pures et Appliquees. 2006
A. Hernández-Montes, L.F. Reséndis O., Hyperbolic area distortion under quasiconformal mappings, J. Inequal. Appl. (2017) 2017: 211. https://doi.org/10.1186/s13660-017-1481-1
R.M. Porter, L.F. Reséndis, A bound for quasisymmetric of polynomials, Complex Variables 3 (1996), 179–191.
R.M. Porter, L.F. Reséndis, Quasiconformally explodable sets, Complex Variables 36 (1998), 379–392.
D. Partyka, K. Sakan, On bi-lipschitz type inequalities for quasiconformal harmonic mappings, Annales Academic Scientiarum Fennicae, Mathematica 32 (2007), 579–594.
