Speaker: George Mathew (Ohio State University, USA)
Date: 16 December 2021
Time: 11:00 am
Venue: LH-1, Mathematics Department
Since the Calabi conjecture was proved in 1978 by S.T. Yau, there has been extensive studies into nonlinear PDEs on complex manifolds.
In this talk, we consider a class of fully nonlinear elliptic PDEs involving symmetric functions of partial Laplacians on Hermitian manifolds.
This is closely related to the equation considered by Székelyhidi-Tosatti-Weinkove in the proof of Gauduchon conjecture. Under fairly general assumptions,
we derive apriori estimates and show the existence of solutions. In addition, we also consider the parabolic counterpart of this equation and
prove the long-time existence and convergence of solutions.