H\'older continuous solutions to Monge-Amp\`ere equations

Autor:	Demailly, Jean-Pierre, Dinew, Slawomir, Guedj, Vincent, Pham, Hoang Hiep, Kolodziej, Slawomir, Zeriahi, Ahmed
Rok vydání:	2011
Předmět:	Mathematics - Complex Variables Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
DOI:	10.1112/blms/bdn092
Popis:	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. Comment: LaTeX, 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1112.1388 Zobrazit plný text záznamu View this record from Arxiv