Prescribed volume forms in Apelli cohomology groups on compact Hermitian manifolds II

时   间：  2022-12-15 16:00 — 17:00

Abstract. Given a  form  on a Hermitian manifold  of dimension , where  is an integer, we study the problem of finding a strongly positive  form in the Apelli cohomology class of with prescribed volume form. For , this is equivalent to the classical Calabi conjecture solved by S.T. Yau in the Kahler case, while for  it corresponds to the Gauduchon conjecture proved by Szekelyhidi-Tosatti- Weinkove more recently. From the PDE point of view, this leads to a new fully nonlinear elliptic equation which falls outside the framework developed by Cafferlli-Nirenberg-Spruck. We shall treat a general class of PDEs which also arise from other geometric problems. The talk is based on work with my student Mathew George.