Stein流形具有非光滑边界强拟凸域上Koppelman-Leray-Norguet公式的拓广式

Abstract

利用Hermitian度量和陈联络,构造拓广的不变积分核,借助Stokes公式,探究Stein流形中具有非光滑边界强拟凸域上Koppelman-Leray-Norguet公式的拓广式及其-方程的连续解,其特点是不含边界积分,从而避免了边界积分的复杂估计,另外该拓广式的特点是含有可供选择的实参数m,m=2,3,…,P(P<+∞),适用范围更加广泛.

By meams of Hermitian metric,Chern connection,and using Stokes' formula,this paper constructed an extended invariant integral kernel,to study the extensional formula of Koppelman-Leray-Norguet formula.We obtain a continuous solution of -equation for a strictly pseudoconvex domain with non-smooth boundary on Stein manifolds,which doesn't involve integral on boundary.Thus we can avoid the complexity estimations of the boundary integrals.Furthermore,there is a real parameter m,m=2,3,…,P(P<+∞),which can be chosen freely in this extensional formula,and its range of application becomes wider.