297 research outputs found
Convexity properties of quasihyperbolic balls on Banach spaces
We study convexity and starlikeness of quasihyperbolic and distance ratio
metric balls on Banach spaces. In particular, problems related to these metrics
on convex domains, and on punctured Banach spaces, are considered
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
Lengths, areas and Lipschitz-type spaces of planar harmonic mappings
In this paper, we establish a three circles type theorem, involving the
harmonic area function, for harmonic mappings. Also, we give bounds for length
and area distortion for harmonic quasiconformal mappings. Finally, we will
study certain Lipschitz-type spaces on harmonic mappings.Comment: 14 page
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