301 research outputs found
On Heinz type inequality and Lipschitz characteristic for mappings satisfying polyharmonic equations
For , suppose that is a -quasiconformal self-mapping of the
unit ball , which satisfies the following: the
polyharmonic equation
, (2)
the boundary conditions
( for
and denotes the unit sphere in
), and , where and are
integers. We first establish a Heinz type inequality on mappings satisfying the
polyharmonic equation. Then we use the obtained results to show that is
Lipschitz continuous, and the estimate is asymptotically sharp as and
for .Comment: 28 page
Schwarz-Pick type estimates of pluriharmonic mappings in the unit polydisk
In this paper, we will give Schwarz-Pick type estimates of arbitrary order
partial derivatives for bounded pluriharmonic mappings defined in the unit
polydisk. Our main results are generalizations of results of Colonna for planar
harmonic mappings in [Indiana Univ. Math. J. 38: 829--840, 1989].Comment: 9 page
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