Authors establish long-time existence and convergence results for general parabolic complex Monge-Ampere type equations on compact Kahler manifolds without convexity or concavity assumptions on the operator.
Fu-Yau Hessian Equations
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abstract
We solve the Fu-Yau equation for arbitrary dimension and arbitrary slope $\alpha'$. Actually we obtain at the same time a solution of the open case $\alpha'>0$, an improved solution of the known case $\alpha'<0$, and solutions for a family of Hessian equations which includes the Fu-Yau equation as a special case. The method is based on the introduction of a more stringent ellipticity condition than the usual $\Gamma_k$ admissible cone condition, and which can be shown to be preserved by precise estimates with scale.
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2019 1verdicts
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Parabolic complex Monge-Ampere equations on compact Kahler manifolds
Authors establish long-time existence and convergence results for general parabolic complex Monge-Ampere type equations on compact Kahler manifolds without convexity or concavity assumptions on the operator.