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Extremal Kaehler metrics and geometric stability

Objetivo

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.

Convocatoria de propuestas

FP7-PEOPLE-2009-IOF
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Coordinador

UNIVERSITA DEGLI STUDI DI PARMA
Aportación de la UE
€ 228 804,70
Dirección
VIA UNIVERSITA 12
43121 PARMA
Italia

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Región
Nord-Est Emilia-Romagna Parma
Tipo de actividad
Higher or Secondary Education Establishments
Contacto administrativo
Claudio Arezzo (Prof.)
Enlaces
Coste total
Sin datos