On stability and continuity of bounded solutions of degenerate complex Monge-Ampère equations over compact Kähler manifolds

16Citations
Citations of this article
8Readers
Mendeley users who have this article in their library.
Get full text

Abstract

We obtain a stability estimate for the degenerate complex Monge-Ampère operator which generalizes a result of Kołodziej (2003) [12]. In particular, we obtain the optimal stability exponent and also treat the case when the right-hand side is a general Borel measure satisfying certain regularity conditions. Moreover, our result holds for functions plurisubharmonic with respect to a big form, thus generalizing the Kähler form setting in Kołodziej (2003) [12]. Independently, we also provide more detail for the proof in Zhang (2006) [18] on continuity of the solution with respect to a special big form when the right-hand side is Lp-measure with p>1. © 2010.

Cite

CITATION STYLE

APA

Dinew, S., & Zhang, Z. (2010). On stability and continuity of bounded solutions of degenerate complex Monge-Ampère equations over compact Kähler manifolds. Advances in Mathematics, 225(1), 367–388. https://doi.org/10.1016/j.aim.2010.03.001

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free