In this project the principal investigator will study problems in the theory of analytic functions of several complex variables. In particular, he will look at the following questions in regard to one-dimensional subvarieties having thin ends: uniqueness, complex tangents, boundary accessibility and the relationship of harmonic measure to linear measure. Further areas of study include function-theoretic hulls of graphs in complex three-space, the boundary behavior of analytic maps, and the finding of disks in certain polynomial hulls in two-space. The theory of functions of several complex variables is a difficult subject in which one's intuition derived from the theory of functions of a single complex variable is often of little help and sometimes even misleading. The principal investigator of this project approaches problems in several complex variables from the point of view of what is called "geometric measure theory". This theory will enable him to continue his important work in the behavior of analytic functions near boundaries and in the convexity of spaces of analytic functions.
