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THE SET OF MEASURES GIVEN BY BOUNDED SOLUTIONS OF THE COMPLEX MONGE–AMPÈRE EQUATION ON COMPACT KÄHLER MANIFOLDS

Published online by Cambridge University Press:  20 July 2005

SŁAWOMIR KOŁODZIEJ
SŁAWOMIR KOŁODZIEJ
Affiliation:
Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Polandkolodzie@im.uj.edu.pl
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Abstract

Consider the image of the Monge–Ampère operator acting on bounded functions, defined on a compact Kähler manifold, whose sum with the local Kähler potential is plurisubharmonic. It is shown that a nonnegative Borel measure belongs to this image if and only if it belongs to the image locally. In particular, those measures form a convex set.

Keywords

32U (primary)32Q15
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 72 , Issue 1 , August 2005 , pp. 225 - 238
Copyright
The London Mathematical Society 2005

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Footnotes

This work was partially supported by KBN grant PO3A 010 19.