### Finite type conditions on reinhardt domains (1996).Finite type conditions on reinhardt domains (1996).

Access Restriction
Open

 Author Fu, Siqi ♦ Isaev, Alexander V. ♦ Krantz, Steven G. Source CiteSeerX Content type Text File Format PDF
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Pseudoconvex Reinhardt Domain ♦ Finite Type Condition ♦ Reinhardt Domain ♦ Boundary Point ♦ Variety Type ♦ Regular Type ♦ Finite Type ♦ Omega Whenever ♦ Log Jz ♦ Eodory Metric ♦ Invariant Object ♦ Domain Omega Ae ♦ Forthcoming Paper ♦ Bergman Kernel Abstract . In this paper we prove that, if p is a boundary point of a smoothly bounded pseudoconvex Reinhardt domain in C n , then the variety type at p is identical to the regular type. In this paper we study the finite type conditions on pseudoconvex Reinhardt domain. We prove that, if p is a boundary point of a smoothly bounded pseudoconvex Reinhardt domain in C n , then the variety type at p is identical to the regular type. In a forthcoming paper, we will study the biholomorphically invariant objects (e.g., the Bergman kernel and metric, the Kobayashi and Carath'eodory metrics) on a pseudoconvex Reinhardt domain of finite type. We first recall some definitions. A domain\Omega ae C n is Reinhardt if (e i 1 z 1 ; : : : ; e in z n ) 2\Omega whenever (z 1 ; : : : ; z n ) 2\Omega and 0 ` j 2; 1 j n. Denote Z j = f(z 1 ; : : : ; z n ) 2 C n ; z j = 0g; for j = 1; : : : ; n. Let Z = S n j=1 Z j . Define L : C n n Z ! R n by L(z 1 ; : : : ; z n ) = (log jz 1 ... Educational Role Student ♦ Teacher Age Range above 22 year Educational Use Research Education Level UG and PG ♦ Career/Technical Study Learning Resource Type Article Publisher Date 1996-01-01