Hölder continuous solutions to Monge-Ampère equations

Details Hölder continuous solutions to Monge-Ampère equations Hölder continuous solutions to Monge-Ampère equations

2011-12-06

arxiv.org/abs/1112.1388v1

Mathematics

Complex Variables

LaTeX, 23 pages

Scientific paper

Let $(X,\omega)$ be a compact K\"ahler manifold. We obtain uniform H\"older regularity for solutions to the complex Monge-Amp\`ere equation on $X$ with $L^p$ right hand side, $p>1$. The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range $\MAH(X,\omega)$ of the complex Monge-Amp\`ere operator acting on $\omega$-plurisubharmonic H\"older continuous functions. We show that this set is convex, by sharpening Ko{\l}odziej's result that measures with $L^p$-density belong to $\MAH(X,\omega)$ and proving that $\MAH(X,\omega)$ has the "$L^p$-property", $p>1$. We also describe accurately the symmetric measures it contains.

Affiliated with

Also associated with

No associations

Rating

Hölder continuous solutions to Monge-Ampère equations 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 Hölder continuous solutions to Monge-Ampère equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hölder continuous solutions to Monge-Ampère equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-382154