Growth and two-point distortion properties for linearly invariant families of locally biholomorphic mappings

Document Type : Original Article

Authors

Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran

Abstract

‎‎This paper establishes lower growth and two-point distortion bounds for linearly invariant families (L.I.F.s) of locally biholomorphic mappings within the unit ball $B^{n}$ in $\mathbb{C}^{n}$‎. ‎We also present lower growth bounds and two-point distortion bounds for affine and linearly invariant families (A.L.I.F.s) of pluriharmonic mappings from the unit ball $B^{n}$ to $\mathbb{C}^{n}$‎. ‎These results build upon recent findings by Pfaltzgraff and Suffridge‎, ‎Graham‎, ‎Kohr and Pfaltzgraff‎, ‎Duren‎, ‎Hamada, and Kohr with an additional condition of quasiregularity on the mappings‎.

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References

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Measure Algebras and Applications
Volume 3, Issue 2 - Serial Number 5
December 2025
Pages 24-36

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