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Modulus of Continuity of Solutions to Complex Monge-Amp\`ere Equations on Stein Spaces

Modulus of Continuity of Solutions to Complex Monge-Amp\`ere Equations on Stein Spaces

In this paper, we study the modulus of continuity of solutions to Dirichlet problems for complex Monge-Amp\`ere equations with $L^p$ densities on Stein spaces with isolated singularities. In particular, we prove such solutions are H\"older continuous outside singular points if the boundary data is H\"older continuous.