#### Vol. 15, No. 4, 2022

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The deformed Hermitian Yang–Mills equation on three-folds

### Vamsi Pritham Pingali

Vol. 15 (2022), No. 4, 921–935
##### Abstract

We prove an existence result for the deformed Hermitian Yang–Mills equation for the full admissible range of the phase parameter, i.e., $\stackrel{^}{𝜃}\in \left(\frac{\pi }{2},\frac{3\pi }{2}\right)$, on compact complex three-folds conditioned on a necessary subsolution condition. Our proof hinges on a delicate analysis of a new continuity path obtained by rewriting the equation as a generalised Monge–Ampère equation with mixed-sign coefficients.

##### Keywords
deformed Hermitian–Yang–Mills equation, generalised Monge–Ampère equation, special Lagrangian equation
##### Mathematical Subject Classification 2010
Primary: 32Q15, 53C07