Geometric plurisubharmonicity and convexity - an introduction

Details Geometric plurisubharmonicity and convexity - an introduction Geometric plurisubharmonicity and convexity - an introduction

2011-11-16

arxiv.org/abs/1111.3875v1

Mathematics

Differential Geometry

Scientific paper

This is an essay on potential theory for geometric plurisubharmonic functions. It begins with a given closed subset G of the Grassmann bundle $G(p,TX)$ of tangent $p$-planes to a riemannian manifold $X$. This determines a nonlinear partial differential equation which is convex but never uniformly elliptic (p < dim X). A surprising number of results in complex analysis carry over to this more general setting. The notions of: a G-submanifold, an upper semi-continuous G-plurisubharmonic function, a G-convex domain, a G-harmonic function, and a G-free submanifold, are defined. Results include a restriction theorem as well as the existence and uniqueness of solutions to the Dirichlet Problem for G-harmonic functions on G-convex domains.

Affiliated with

Also associated with

No associations

Rating

Geometric plurisubharmonicity and convexity - an introduction does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometric plurisubharmonicity and convexity - an introduction, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric plurisubharmonicity and convexity - an introduction will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-68921