Seminar on Geometric Complex Analysis

Seminar information archive ~04/15Next seminarFuture seminars 04/16~

Date, time & place Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Kengo Hirachi, Shigeharu Takayama


10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Atsushi Hayashimoto (National Institute of Technology, Nagano College)
Proper holomorphic mappings and generalized pseudoellipsoids (JAPANESE)
[ Abstract ]
We study the classification of proper holomorphic mappings between generalized pseudoellipsoids of different dimensions.

Huang proved some classification theorems of proper holomorphic mappings between balls of different dimensions, which are called gap theorems. Our present theorems are their weakly pseudoconvex versions.

In the theorem, classified mapping is so-called a variables splitting mapping and each component is derived from a homogeneous proper polynomial mapping between balls.

The essential methods are the ''good'' decompositions of CR vector bundle and reduction the mapping under consideration to the mapping of balls. By this reduction, we can apply Huang's gap theorem.