Pluripotential Theory, Hulls and Foliations

• Applicant: Professor Dr. Nikolay Shcherbina
• Subject Area: Mathematics
• Term: from 2009 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 125787714

Classical potential theory was built in the first part of the last century and its development was motivated mainly (but not only) by interests of electro-physics. Pluripotential theory is much younger and its basic results were obtained in 70’s - 80’s in the fundamental works of Bedford, Taylor, Sadullaev and others. Interest to this area and its importance are determined both by the needs of complex analysis and by applications to other fields, e.g. to dynamical systems. While many fundamental results of this theory are already well understood, we will address some important open problems concerning the structure of pluripolar sets and properties of the pluricomplex Green function. A second part of the project is devoted to the study of polynomial and rational hulls which appear naturally in the classical problem of polynomial and rational approximation. Despite the importance of these notions, the structure of polynomial and rational hulls is far from being understood even in the case of compact sets in Cn and is basically not understood at all for unbounded sets. Financial support for this project is aimed at fostering international collaboration, exchange of ideas, and especially (and foremost) at promoting young mathematicians.

• DFG Programme: Research Grants