426 research outputs found
H\"older continuous solutions to complex Hessian equations
We prove the H\"older continuity of the solution to complex Hessian equation
with the right hand side in , , , in a
-strongly pseudoconvex domain in under some additional
conditions on the density near the boundary and on the boundary data.Comment: 19 pages. Added Theorem 3.7: when the boundary is Holder continuous,
there exists a Holder continuous -sh extension to the domai
Subsolution theorem for the complex Hessian equation
We prove the subsolution theorem for the complex Hessian equations in a
smoothly bounded strongly -pseudoconvex domain, , in \bC^n.Comment: 18 pages. Corrected typos. To appear in Universitatis Iagellonicae
Acta Mathematic
Stability and regularity of solutions of the Monge-Amp\`ere equation on Hermitian manifolds
We prove stability of solutions of the complex Monge-Amp\`ere equation on
compact Hermitian manifolds, when the right hand side varies in a bounded set
in and it is bounded away from zero. Such solutions are shown to be
H\"older continuous. As an application we extend a recent result of
Sz\'ekelyhidi and Tosatti on K\"ahler-Einstein equation from K\"ahler to
Hermitian manifolds.Comment: v4 final version incorporated the referee repor
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