Volume Approximations of Strongly Pseudoconvex Domains

In convex geometry, the Blaschke surface area measure on the boundary of a convex domain can be interpreted in terms of the complexity of approximating polyhedra. This approach is formulated in the holomorphic setting to establish an alternate interpretation of Fefferman’s hypersurface measure on boundaries of strongly pseudoconvex domains in C2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}^2$$\end{document}. In particular, it is shown that Fefferman’s measure can be recovered from the Bergman kernel of the domain.