The deformed Hermitian Yang–Mills equation on three-folds

Pingali, Vamsi Pritham

doi:10.2140/apde.2022.15.921

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The deformed Hermitian Yang–Mills equation on three-folds

Vamsi Pritham Pingali

Vol. 15 (2022), No. 4, 921–935

DOI: 10.2140/apde.2022.15.921

Abstract

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

Keywords

deformed Hermitian–Yang–Mills equation, generalised Monge–Ampère equation, special Lagrangian equation

Mathematical Subject Classification 2010

Primary: 32Q15, 53C07

Milestones

Received: 4 October 2019

Revised: 5 November 2020

Accepted: 31 December 2020

Published: 3 September 2022

Authors

Vamsi Pritham Pingali
Department of Mathematics Indian Institute of Science Bangalore India

Vol. 15, No. 4, 2022