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<p>We introduce a parabolic analogue of the elliptic split-type Monge-Ampère equation developed by Fang and the author, extending Streets’ twisted Monge-Ampère equation. The resulting equation is fully nonlinear and non-concave. We prove long-time existence for equations whose exponents are not too far apart and give conditions for convergence to the twisted Monge-Ampère when the exponents approach each other. Applications include long-time convergence on Kähler backgrounds and reduction to the twisted Monge-Ampère equation under curvature assumptions.</p>

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The parabolic split-type Monge-Ampère on split tangent bundle surfaces

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  • 出版模式：

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  • 发表日期：

    2026年3月14日

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  • Joshua Jordan

摘要

We introduce a parabolic analogue of the elliptic split-type Monge-Ampère equation developed by Fang and the author, extending Streets’ twisted Monge-Ampère equation. The resulting equation is fully nonlinear and non-concave. We prove long-time existence for equations whose exponents are not too far apart and give conditions for convergence to the twisted Monge-Ampère when the exponents approach each other. Applications include long-time convergence on Kähler backgrounds and reduction to the twisted Monge-Ampère equation under curvature assumptions.