Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-09T07:41:48.989Z Has data issue: false hasContentIssue false
  • English
  • Français

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, [email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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