Short Course

S. Ali Aleyasin, Institute for Research in Fundamental Sciences (IPM)
Calabi Problem: Old and New

In this short course, we shall first state the classical Calabi problem and the solutions of S-T. Yau and T. Aubin to this conjecture in the case of non-positive first Chern class. This will require reviewing some basic K\"ahler goemetry and linear analysis on closed compact manifolds.‎

‎We will, then, move on to deriving the elliptic estimates required for solving the corresponding complex Monge-Amp\`ere equations. Finally, we shall discuss the new generalisations of these results to the case of non-compact and singular manifolds, detailing the case of edge-cone manifolds.

Date & Time: 
Tuesday, July 26, 2016, 9:00 - 10:30 & 11:00 - 12:30 & 14:00 - 15:30
Wednesday, July 27, 2016, 9:00 - 10:30 & 11:00 - 12:30
Lecture Hall 1, Niavaran Building, IPM