Lower Bounds on the Kobayashi Metric Near a Point of Infinite Type

Abstract

Under a potential-theoretical hypothesis named f-property which holds for all pseudoconvex domains of finite type and many examples of infinite type, we give a new method for constructing a family of bumping functions and hence plurisubharmonic peak functions with good estimates. The rate of lower bounds on the Kobayashi metric follows by the estimates of peak functions. The application to the continuous extendibility of proper holomorphic maps is given.