CRC 1442 - B05: Scalar curvature in Kähler geometry

Basic data for this project

Type of projectSubproject in DFG-joint project hosted at University of Münster
Duration at the University of Münster01/07/2021 - 30/06/2024 | 1st Funding period

Description

In this project we propose to study the degeneration of Kähler manifolds with constant or bounded scalar curvature under a non-collapsing assumption. For Riemannian manifolds of bounded sectional curvature, this is the content of the classical Cheeger-Gromov convergence theory from the 1970s. For Riemannian manifolds of bounded Ricci curvature, definitive results were obtained by Cheeger-Colding-Naber in the past 10-20 years, with spectacular applications to the Kähler-Einstein problem on Fano manifolds. Very little is currently known under only a scalar curvature bound even in the Kähler case. We propose to make progress in two different directions: (I) Gather examples of weak convergence phenomena related to the stability of the Positive Mass Theorem for Kähler metrics and to Taubes' virtually infinite connected sum construction for ASD 4-manifolds. (II) Study uniqueness and existence of constant scalar curvature Kähler metrics on non-compact or singular spaces by using direct PDE methods.

KeywordsGeometry; Mathematics
DFG-Gepris-IDhttps://gepris.dfg.de/gepris/projekt/465078454
Funding identifierSFB 1442/1 – 2021 | DFG project number: 427320536
Funder / funding scheme
  • DFG - Collaborative Research Centre (SFB)

Project management at the University of Münster

Hein, Hans-Joachim
Mathematical Institute
Professorship of theoretical mathematics (Prof. Hein)
Santoro, Bianca
Mathematical Institute

Applicants from the University of Münster

Hein, Hans-Joachim
Mathematical Institute
Professorship of theoretical mathematics (Prof. Hein)

Research associates from the University of Münster

Klemmensen, Johan Jacoby
Mathematical Institute