We study Hölder continuity of solutions to the Monge-Ampère equations on compact Kähler manifolds. T. C. Dinh, V.A. Nguyen and N. Sibony have shown that the measure is moderate if is Hölder continuous. We prove a theorem which is a partial converse to this result.
We establish the comparison principle in the class . The result obtained is applied to the Dirichlet problem in .
We give a characterization for boundedness of plurisubharmonic functions in the Cegrell class ℱ.
We study boundary values of functions in Cegrell’s class .
We prove that if in Cₙ-capacity then . This result is used to consider the convergence in capacity on bounded hyperconvex domains and compact Kähler manifolds.
We study the weighted Bernstein-Markov property for subsets in ℂⁿ which might not be bounded. An application concerning approximation of the weighted Green function using Bergman kernels is also given.
The energy class is studied for 0 < p < 1. A characterization of certain bounded plurisubharmonic functions in terms of and its pluricomplex p-energy is proved.
We establish some results on ω-pluripolarity and complete ω-pluripolarity for sets in a compact Kähler manifold X with fundamental form ω. Moreover, we study subextension of ω-psh functions on a hyperconvex domain in X and prove a comparison principle for the class 𝓔(X,ω) recently introduced and investigated by Guedj-Zeriahi.
Let be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on with right hand side, . The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range of the complex Monge-Ampère operator acting on -plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with -density belong to and proving that has the...
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