Geodesic
Hölder continuous solutions to Monge–Ampère equations
Journal of the European Mathematical Society, Tome 16 (2014) no. 4, pp. 619-647 Cet article a éte moissonné depuis la source EMS Press

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Let (X,ω) be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on X with Lp 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,ω) of the complex Monge-Ampère operator acting on ω-pluri-subharmonic Hölder continuous functions. We show that this set is convex, by sharpening\break Ko\l odziej's result that measures with Lp-density belong to MAH(X,ω) and proving that MAHX,ω) has the “Lp-property”, p>1. We also describe accurately the symmetric measures it contains.
DOI : 10.4171/jems/442
Classification : 32-XX, 00-XX, 53-XX
Keywords: Monge–Ampère operator, Kähler manifold, pluripotential theory, Hölder continuity 
@article{JEMS_2014_16_4_a0,
     author = {Jean-Pierre Demailly and S{\l}awomir Dinew and Vincent Guedj and Pham Hoang Hiep and S{\l}awomir Ko{\l}odziej and Ahmed Zeriahi},
     title = {H\"older continuous solutions to {Monge{\textendash}Amp\`ere} equations},
     journal = {Journal of the European Mathematical Society},
     pages = {619--647},
     year = {2014},
     volume = {16},
     number = {4},
     doi = {10.4171/jems/442},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/442/}
}
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%A Sławomir Kołodziej
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%R 10.4171/jems/442
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Jean-Pierre Demailly; Sławomir Dinew; Vincent Guedj; Pham Hoang Hiep; Sławomir Kołodziej; Ahmed Zeriahi. Hölder continuous solutions to Monge–Ampère equations. Journal of the European Mathematical Society, Tome 16 (2014) no. 4, pp. 619-647. doi: 10.4171/jems/442

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