Glasnik Matematicki, Vol. 34, No.2 (1999), 203-210.
CONVEX MAPPINGS IN SEVERAL COMPLEX VARIABLES
Hidetaka Hamada and Gabriela Kohr
Faculty of Engineering, Kyushy Kyoritsu University, 1-8 Jiyugaoka,
Yahatanishi-Ku, Kitakyushu 807-8585, Japan
e-mail: hamada@kyukyo-u.ac.jp
Faculty of Engineering, Babes-Bolyai University,
1 M. Kogalniceanu Str., 3400 Cluj-Napoka, Romania
e-mail: gkohr@math.ubbcluj.ro
Abstract. Let B be the unit ball of
Cn
with respect to an arbitrary norm. We will give a
sufficient condition for a local diffeomorphism
of C1 class on B to be univalent
and to have a convex image. Finally, we present an
application on the complex ellipsoid
B(p1, ... , pn),
where p1, ... , pn
≥ 1.
1991 Mathematics Subject Classification.
32H, 30C45.
Key words and phrases. Convexity, starlikeness,
diffeomorphism.
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