Properties of Some Classes of Planar Harmonic and Planar Biharmonic Mappings

S. H. Chen1, Saminathan Ponnusamy2, X. Wang1
1Department of Mathematics, Hunan Normal University, Changsha, 410081 Hunan, People’s Republic of China
2Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India

Tóm tắt

Từ khóa


Tài liệu tham khảo

Abdulhadi Z., Abu Muhanna Y.: Landau’s theorem for biharmonic mappings. J. Math. Anal. Appl. 338, 705–709 (2008)

Abdulhadi Z., Abu Muhanna Y., Khoury S.: On univalent solutions of the biharmonic equations. J. Inequal. Appl. 5, 469–478 (2005)

Chen H., Gauthier P.M., Hengartner W.: Bloch constants for planar harmonic mappings. Proc. Am. Math. Soc. 128, 3231–3240 (2000)

Chuaqui M., Hernández R.: Univalent harmonic mappings and linearly connected domains. J. Math. Anal. Appl. 332, 1189–1194 (2007)

Clunie J.G., Sheil-Small T.: Harmonic univalent functions. Ann. Acad. Sci. Fenn. Ser. A. I. 9, 3–25 (1984)

Colonna F.: The Bloch constant of bounded harmonic mappings. Indiana Univ. Math. J. 38, 829–840 (1989)

Dorff M., Nowak M.: Laudau’s theorem for planar harmonic mappings. Comput. Methods Funct. Theory. 4, 151–158 (2004)

Duren P.: Harmonic Mappings in the Plane. Cambridge University Press, Cambridge (2004)

Heinz E.: On one-to-one harmonic mappings. Pacific J. Math. 9, 101–105 (1959)

Liu M.Sh.: Laudau’s theorem for biharmonic mappings. Complex Var. Theory Appl. 53, 843–855 (2008)

Pommerenke Ch.: Boundary behaviour of conformal maps, Grunglehren Math. Wiss, vol. 299. Springer, Berlin (1992)

Rickman S.: Quasiregular Maps. Springer, Berlin (1993)

Vuorinen, M.: Conformal geometry and quasiregular mappings. Lecture Notes in Mathematics, vol. 1319. Springer, Berlin (1988)

Xinzhong H.: Estimates on Bloch constants for planar harmonic mappings. J. Math. Anal. Appl. 337, 880–887 (2008)