Supercritical deformed Hermitian-Yang-Mills equation
Gao Chen
TL;DR
This paper establishes a precise criterion for solving the supercritical deformed Hermitian-Yang-Mills equation, linking it to mirror symmetry and confirming a conjecture about special Lagrangian submanifolds on Calabi-Yau manifolds.
Contribution
It provides a necessary and sufficient condition for solvability using integrals on subvarieties, advancing understanding of mirror symmetry and special Lagrangian geometry.
Findings
Criteria for solvability of the equation
Confirmation of the mirror Thomas-Yau conjecture
Connection to special Lagrangian submanifolds
Abstract
In this paper, we provide a necessary and sufficient condition for the solvability of the supercritical deformed Hermitian-Yang-Mills equation using integrals on subvarieties. This result confirms the mirror version of the Thomas-Yau conjecture about special Lagrangian submanifolds on Calabi-Yau manifolds.
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