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

2025/07/09 by Jordan, Joshua
#35K55 #53C55 (Primary) 35B65 #53C56 (Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.07084

Abstract

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.

Citations

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