A note on the deformed Hermitian Yang-Mills PDE
Differential Geometry
2018-03-02 v4 Mathematical Physics
math.MP
Abstract
We prove a priori estimates for a generalised Monge-Amp\`ere PDE with "non-constant coefficients" thus improving a result of Sun in the K\"ahler case. We apply this result to the deformed Hermitian Yang-Mills (dHYM) equation of Jacob-Yau to obtain an existence result and a priori estimates for some ranges of the phase angle assuming the existence of a subsolution. We then generalise a theorem of Collins-Sz\`ekelyhidi on toric varieties and use it to address a conjecture of Collins-Jacob-Yau.
Keywords
Cite
@article{arxiv.1509.00943,
title = {A note on the deformed Hermitian Yang-Mills PDE},
author = {Vamsi P. Pingali},
journal= {arXiv preprint arXiv:1509.00943},
year = {2018}
}
Comments
Final version. 14 pages. To appear in Complex Variables and Elliptic equations