Domains in C n with a piecewise Levi flat boundary which possess a noncompact automorphism group

A characterization of domains in C 2 with noncompact automorphism group

“…The same conclusion was arrived at in [39] under the weaker hypothesis that the boundary of D is strongly pseudoconvex only near p ∞ . A systematic study of this phenomenon for more general pseudoconvex domains was initiated by Greene-Krantz and we refer the reader to [2], [3], [4], [5], [6], [7], [17], [20], [29] and [30] which provide a panoramic view of some of the known results in this direction. The survey articles [27] and [31] contain an overview of the techniques that are used and provide a comprehensive list of relevant references as well.…”

On a theorem of Paul Yang on negatively pinched bisectional curvature

“…However, cannot be biholomorphic to D 2 [Fridman 1978]. Likewise, is not homogeneous; if it were, then it would be biholomorphic to D 2 [Kim 1992]. …”

On the scaling methods by Pinchuk and Frankel

“…These techniques have been developed further by many authors and have become an important tool to prove the results of [11], [2], [9] and others.…”