Characterization of Monge-Ampere measures with Holder continuous potentials

2012/04/22 by Dinh, Tien-Cuong, Nguyen, Viet-Anh
#32U #32W20 #53C55 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1204.4883

Abstract

We show that the complex Monge-Ampere equation on a compact Kaehler manifold (X,ω) of dimension n admits a Holder continuous omega-psh solution if and only if its right-hand side is a positive measure with Holder continuous super-potential. This property is true in particular when the measure has locally Holder continuous potentials or when it belongs to the Sobolev space W^{2n/p-2+epsilon,p}(X) or to the Besov space B^epsilon-2_∞,∞(X) for some epsilon>0 and p>1.

Related

• Families of Monge-Ampere measures with Holder continuous potentials
• The complex Sobolev Space and Hölder continuous solutions to Monge-Ampère equations
• Hölder continuous potentials on manifolds with partially positive curvature
• Hölder continuous solutions of the Monge-Ampère equation on compact Hermitian manifolds
• Continuous solutions to Monge-Amp `ere equations on Hermitian manifolds\n for measures dominated by capacity