Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator
We find a bounded solution of the non-homogeneous Monge-Ampère equation under very weak assumptions on its right hand side.
Weak solutions of equations of complex Monge-Ampère type
We prove some existence results for equations of complex Monge-Ampère type in strictly pseudoconvex domains and on Kähler manifolds.
Jung's type theorem for polynomial transformations of ℂ²
We prove that among counterexamples to the Jacobian Conjecture, if there are any, we can find one of lowest degree, the coordinates of which have the form + terms of degree < m+n.
A regularity theorem for the complex Monge-Ampère equation in ℂPⁿ
regularity of the solutions of the complex Monge-Ampère equation in ℂPⁿ with the n-root of the right hand side in is proved.
Hölder continuous solutions to Monge–Ampère equations
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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