# Hölder continuous solutions to Monge–Ampère equations

Jean-Pierre Demailly; Sławomir Dinew; Vincent Guedj; Pham Hoang Hiep; Sławomir Kołodziej; Ahmed Zeriahi

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 4, page 619-647
- ISSN: 1435-9855

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topDemailly, Jean-Pierre, et al. "Hölder continuous solutions to Monge–Ampère equations." Journal of the European Mathematical Society 016.4 (2014): 619-647. <http://eudml.org/doc/277319>.

@article{Demailly2014,

abstract = {Let $(X,\omega )$ be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère 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 $(X,\omega )$ of the complex Monge-Ampère operator acting on $\omega $-plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with $L^p$-density belong to $(X,\omega )$ and proving that $(X,\omega )$ has the "$L^p$-property”, $p>1$. We also describe accurately the symmetric measures it contains.},

author = {Demailly, Jean-Pierre, Dinew, Sławomir, Guedj, Vincent, Hiep, Pham Hoang, Kołodziej, Sławomir, Zeriahi, Ahmed},

journal = {Journal of the European Mathematical Society},

keywords = {Monge–Ampère operator; Kähler manifold; pluripotential theory; Hölder continuity; Monge-Ampère operator; Kähler manifold; pluripotential theory; Hölder continuity},

language = {eng},

number = {4},

pages = {619-647},

publisher = {European Mathematical Society Publishing House},

title = {Hölder continuous solutions to Monge–Ampère equations},

url = {http://eudml.org/doc/277319},

volume = {016},

year = {2014},

}

TY - JOUR

AU - Demailly, Jean-Pierre

AU - Dinew, Sławomir

AU - Guedj, Vincent

AU - Hiep, Pham Hoang

AU - Kołodziej, Sławomir

AU - Zeriahi, Ahmed

TI - Hölder continuous solutions to Monge–Ampère equations

JO - Journal of the European Mathematical Society

PY - 2014

PB - European Mathematical Society Publishing House

VL - 016

IS - 4

SP - 619

EP - 647

AB - Let $(X,\omega )$ be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère 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 $(X,\omega )$ of the complex Monge-Ampère operator acting on $\omega $-plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with $L^p$-density belong to $(X,\omega )$ and proving that $(X,\omega )$ has the "$L^p$-property”, $p>1$. We also describe accurately the symmetric measures it contains.

LA - eng

KW - Monge–Ampère operator; Kähler manifold; pluripotential theory; Hölder continuity; Monge-Ampère operator; Kähler manifold; pluripotential theory; Hölder continuity

UR - http://eudml.org/doc/277319

ER -

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