The deformed Hermitian Yang-Mills equation on three-folds

Abstract

We prove an existence result for the deformed Hermitian Yang-Mills equation for the full admissible range of the phase parameter, i.e., $\hat{\theta }\in (\frac{\pi }{2},\frac{3\pi }{2})$, 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.

Corrected a few minor errors

References in corpus (2)

• Supercritical deformed Hermitian-Yang-Mills equation
• A rigid theorem for deformed Hermitian-Yang-Mills equation

Cited by in corpus (7)

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• A new flow solving the LYZ equation in Kähler geometry
• The deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds
• Chern number inequalities of deformed Hermitian-Yang-Mills metrics on four dimensional Kaehler manifolds