Families of Strictly Pseudoconvex Domains and Peak Functions

Abstract

We prove that given a family $\left(G_t\right)$ of strictly pseudoconvex domains varying in $C^2$ topology on domains, there exists a continuously varying family of peak functions $h_{t,\zeta }$ for all $G_t$ at every $\zeta \in \partial G_t$ .

Keywords: Peak functions; Peak points; Strictly pseudoconvex domains.