Analysis and Geometry in Several Complex Variables

• Applicant: Professor Dr. Stefan Nemirovski
• Subject Area: Mathematics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 573467810

1) Wider research context In our proposal, we gather several important problems in the analysis and geometry of Several Complex Variables. The proposal brings together three European groups, each with a different emphasis: the University of Vienna, the Jagiellonian University, and the University of Wuppertal. Our unique blend of people specializing in different aspects of analysis and geometry will allow us to bring new insights to some classical problems. 2) Research questions In the proposal, we formulate 11 problem areas (labeled WP A-J). WP A (Variations around the Lempert theorem) addresses questions about the uniqueness of invariant distances and applications to holomorphic maps. WP B (Bergman functions) proposes problems on the zeroes of the Bergman kernel and the Wiegerinck problem. WP C (Carnot–Charatheodory metric for finite type pseudoconvex domains) is mainly concerned with the Balogh-Bonk estimate on finite type domains. WP D (Uniformization problems and ball quotients) studies the Steinness of ball quotients. WP E (Invariant metrics on the boundary) is interested in the invariant metric on the boundary of a strictly pseudoconvex domain. WP F (Kobayashi and Bergman hyperbolicity of model domains) studies hyperbolicity of (unbounded) model domains. WP G (Graphs over spheres) addresses issues arising in the study of small sphere deformations. WP H (Real holomorphic vector fields) is interested in characterizing the existence of real holomorphic vector fields on hermitian manifolds. WP I (Volumes of sublevel sets of plurisubharmonic functions) addresses questions about the Brezis-Merle inequality. WP J (Pluripotential theory and the Monge-Ampere equation) studies pluripotential theory in worm domains and isoperimetric inequalities. WP K (Borel maps) is interested in functional-analytic characterizations of properties of polynomially convex sets.

• DFG Programme: Research Grants
• International Connection: Austria, Poland
• Partner Organisation: Narodowe Centrum Nauki (NCN)
• Cooperation Partners: Professor Dr. Bernhard Lamel; Professor Dr. Wlodzimierz Zwonek
• Co-Investigators: Professor Dr. Jean Ruppenthal; Professor Dr. Nikolay Shcherbina