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.

arXiv commentCorrected a few minor errors

References in corpus (7)

• (1,1) forms with specified Lagrangian phase: A priori estimates and algebraic obstructions
• Supercritical deformed Hermitian-Yang-Mills equation
• On J-equation
• Moment maps, nonlinear PDE, and stability in mirror symmetry
• A generalised Monge-Ampère equation
• $I$-properness of Mabuchi's $K$-energy
• A rigid theorem for deformed Hermitian-Yang-Mills equation

Cited by in corpus (7)

• Stability and the deformed Hermitian-Yang-Mills equation
• Collapsing of the line bundle mean curvature flow on Kähler surfaces
• Tan-concavity property for Lagrangian phase operators and applications to the tangent Lagrangian phase flow
• Deformed Hermitian-Yang-Mills Equation on Compact Hermitian Manifolds
• 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