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The deformed Hermitian Yang-Mills equation on three-folds

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arxiv 1910.01870 v4 pith:JE5MJQ7W submitted 2019-10-04 math.DG math-phmath.APmath.MP

Vamsi Pritham Pingali This is my paper · ORCID
classification math.DGmath-phmath.APmath.MP
keywords equationdeformedfrachermitianthree-foldsyang-millsadmissibleanalysis
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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-Amp\`ere equation with mixed sign coefficients.

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  1. A remark for fully non-linear elliptic equations on compact almost Hermitian manifolds

    math.AP 2025-06 conditional novelty 5.0 of 10

    Existence of solutions for fully nonlinear elliptic equations on compact almost Hermitian manifolds is established under a sub-slope condition, with applications to the Hessian quotient and deformed Hermitian-Yang-Mil...

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