Speaker: Biao Ma (Peking University)
Time: 10:00-11:00, Oct 27, 2023
Room: room 414, Shanghai lnstitute for Advanced Studies, USTC
We introduce a fully nonlinear PDE on Kahler manifolds with a differential form \Lambda. Such PDE unifies several important equations in complex geometry including Monge-Ampere equation, J-equation, and deformed Hermitian Yang-Mills (dHYM) equation. Based on G.Chen's breakthrough on J-equation and dHYM equation, we prove analytical and algebraic criterions for the solvability of the equation, assuming certain positivity conditions on \Lambda. As an application of our results, we prove a conjecture of Collins-Jacob-Yau for dHYM equation with small global phase. This is a joint work with Professor Hao Fang.
