Fachbereich Mathematik und Informatik FB 10

Current Projects	• CRC 1442: Geometry: Deformation and Rigidity - B05: Scalar curvature in Kähler geometry 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. online
E-Mail	j dot klemmensen at uni-muenster dot de
Phone	+49 251 83-36873
FAX	+49 251 83-32711
Room	110.023
Secretary	Sekretariat Huppert Frau Sandra Huppert Telefon +49 251 83-33748 Fax +49 251 83-32711 Zimmer 411
Address	Herr Johan Klemmensen Mathematisches Institut Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland
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