Abstract
We introduce a fully nonlinear PDE with a differential form, which unifies several important equations in Kähler geometry including Monge-Ampère equations, J-equations, inverse σk equations, and deformed Hermitian Yang-Mills (dHYM) equations. We pose some natural positivity conditions on Λ, and prove analytical and algebraic criterion for the solvability of the equation. Our results generalize previous works of G. Chen, J. Song, Datar-Pingali and others. As an application, we prove a conjecture of Collins-Jacob-Yau for dHYM equations with small global phase.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Similar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.