Monge-Ampère equations on compact Hessian manifolds
نویسندگان
چکیده
We consider degenerate Monge-Ampere equations on compact Hessian manifolds. establish compactness properties of the set normalized quasi-convex functions and show local global comparison principles for twisted operators. then use Perron method to solve whose RHS involves an arbitrary probability measure, generalizing works Cheng-Yau, Delanoe, Caffarelli-Viaclovsky Hultgren-Onnheim. The intrinsic approach we develop should be useful in deriving similar results mildly singular varieties, line with Strominger-Yau-Zaslow conjecture.
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ژورنال
عنوان ژورنال: Annali della Scuola normale superiore di Pisa. Classe di scienze
سال: 2022
ISSN: ['0391-173X', '2036-2145']
DOI: https://doi.org/10.2422/2036-2145.202106_017