=
Pluricomplex
Poisson kernel and
horospheres
for strongly convex domains
Professor Giorgio Patrizio
Università deg=
li
Ab=
stract
For
a bounded strongly convex domain in the complex space we construct a soluti=
on of
a homogeneous complex MongeAmpère equation with a simple pole at a
boundary point and whose level sets are boundaries of horospheres. We prove
that such a solution enjoys many properties of the classical Poisson kernel=
in
the unit disc and thus deserves to be called the pluricomplex Poisson kerne=
l.
We discuss extremality properties, relations with the pluricomplex Green
function, uniqueness in terms of the associated foliation and boundary
behaviors and obtain explicit reproducing formulas for plurisubharmonic
functions. Among other things, we show that the biholomorphisms between
strongly convex domains are exactly those maps which preserves our solution=
.
Date:<= o:p> 
April 9, 2008 (Wednesday) 
Time:<= o:p> 
2:30 – 3:30pm 
Place:=

Room 517, Meng Wah Complex, HKU 

All are
welcome 
