Kobayashi metric version of Wong-Rosay Theorem

Seshadri and Verma have shown that a bounded strongly convex domain (with a very smooth boundary such as six times continuously-differentiable) in complex Euclidean space of arbitrary finite dimension possessing a non-compact group of continuous Kobayashi distance preserving selfmaps is necessarily biholomorphic to the open unit ball of the same dimension. This was an exotic, and rather surprising a result in the study of automorphism groups of pseudoconvex domains. On the other hand, the same conclusion should be obtainable with a strongly pseudoconvex domain -- this was what the experts in the line of research expects. I would like to report the very recent result from my collaboration with Steven G. Krantz: Let W be a bounded, strongly pseudoconvex domain with a six times continuously differentiable boundary. If its Kobayashi isometry group is not compact, then W is biholomorphic to the open unit ball with the same dimension.