  The central purpose of the present paper is to study boundary behavior of
squeezing functions on bounded domains. We prove that the squeezing function of
a strongly pseudoconvex domain tends to 1 near the boundary. In fact, such an
estimate is proved for the squeezing function on any domain near its globally
strongly convex boundary points. We also study the stability of squeezing
functions on a sequence of bounded domains, and give comparisons of intrinsic
measures and metrics on bounded domains in terms of squeezing functions. As
applications, we give new and simple proofs of several well known results about
geometry of strongly pseudoconvex domains, and prove that all Cartan-Hartogs
domains are homogenous regular. Finally, some related problems that ask for
further study are proposed.
