{"paper":{"title":"H\\\"older continuous solutions to Monge-Amp\\`ere equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Ahmed Zeriahi (IMT), Hoang Hiep Pham (IF), Jean-Pierre Demailly (IF), Slawomir Dinew (IMT), Slawomir Kolodziej (IMT), Vincent Guedj (IMT)","submitted_at":"2011-12-06T19:57:10Z","abstract_excerpt":"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 \"$L^p$-pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1388","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}