The foundations of p-convexity and p-plurisubharmonicity in riemannian geometry

Details The foundations of p-convexity and p-plurisubharmonicity in riemannian geometry The foundations of p-convexity and p-plurisubharmonicity in riemannian geometry

2011-11-16

arxiv.org/abs/1111.3895v1

Mathematics

Differential Geometry

Scientific paper

In this paper we systematically study the notions of a p-plurisubharmonic function and p-convexity in riemannian geometry. New facts of a basic nature are established. In addition, local p-convexity is shown to imply p-convexity (analogous to the Levi problem in complex analysis). A level-p version of the Monge-Ampere operator is introduced. The solution to the Dirichlet problem for all branches of the homogeneous level-p Monge-Ampere equation is given.

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