The parabolic split-type Monge-Ampère on split tangent bundle surfaces
Abstract
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.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Calculus of Variations and Partial Differential Equations
- Volume
- 65
- Issue
- 4
- Publication date
- 14 March 2026
- Language
- EN