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Geometry & Topology Seminar

Title: Fully nonlinear PDEs on complex manifolds
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.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 21 Jun 2024