Constructing strictly plurisubharmonic functions on the complexification of certain non-compact manifolds

Details Constructing strictly plurisubharmonic functions on the complexification of certain non-compact manifolds Constructing strictly plurisubharmonic functions on the complexification of certain non-compact manifolds

2011-08-30

arxiv.org/abs/1108.5846v1

Mathematics

Complex Variables

18 pages

Scientific paper

The purpose of this paper is to extend a strictly convex function $f$ on $M$ to a \sps \ function $\hat f$ on its complexification $\frak D_{M}.$ If there existed a $\pi$-invariant \sps\ function in $\frak D_M$, its restriction to $M$ must be strictly convex. When $M$ is a symmetric space of non-compact type, we show that the $\pi$-invariant lifting of any strictly convex function in $M$ is \sps\ in $\frak D_{M}.$ As a byproduct, \sps\ exhaustions of the disk bundle $T^rM$ can be constructed in an explicit way

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