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CAMEGEST - Extremal Kaehler metrics and geometric stability

  • 22933
  • CORDIS - PROJECTS 21/10/2010

The problem of finding canonical Kaehler metrics on compact manifolds is central in Kaehler geometry. Since the pioneering work of Calabi, the existence problem for Kaehler-Einstein (and more generally constant scalar curvature, or even extremal Kaehler) metrics has attracted considerable attention. In this circle of ideas the most fascinating problem is represented by the so-called Yau-Tian-Donaldson conjecture, which predict the equivalence between the K-polystability of a polarized manifold and the existence of a constant scalar curvature (or more generally extremal) Kaehler metric in the polarization class. In this vein we propose the following three main research objectives:

- first, find an algebraic criterion for K-stability of polarized manifolds;

- second, study the effect of symplectic reduction on relative K-stability;

- third study the Calabi flow (in particular on toric manifolds) adapting the La Nave-Tian and Arezzo-La Nave approach to the Kahhler-Ricci flow.

We propose to develop the research at Princeton University, under the superfision of prof. G. Tian, and Parma University, under the supervision of prof. C. Arezzo.

Start date: 2010-09-15
End date: 2013-09-14

Duration: 36 months

Project Reference: 255579

Project cost: 228804.00 euro
Project Funding: 228804.00 euro

Subprogramme Area: FP7-PEOPLE-2009-IOF Marie Curie International Outgoing Fellowships for Career Development
Contract type: International Outgoing Fellowships (IOF)


Quadro di finanziamento
  • 7FP-PEOPLE : PERSONE: programma specifico del Settimo programma quadro (2007-2013) di attività comunitarie di ricerca, sviluppo tecnologico e dimostrazione
Area di interesse
  • Unione Europea