MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C97642.635F9F60" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C97642.635F9F60 Content-Location: file:///C:/2F56758F/GEO-Patrizio.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Institute of Mathematical Research
Geometry Seminar


Pluricomplex Poisson kernel and

horospheres for strongly convex domains


Professor Giorgio Patrizio

Università deg= li Studi di Firenze, Italy



Ab= stract


For a bounded strongly convex domain in the complex space we construct a soluti= on of a homogeneous complex Monge-Ampère 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


Room 517, Meng Wah Complex, HKU




All are welcome



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