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.
A flow of conformally balanced metrics with K\"ahler fixed points
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abstract
While the Anomaly flow was originally motivated by string theory, its zero slope case is potentially of considerable interest in non-Kahler geometry, as it is a flow of conformally balanced metrics whose stationary points are precisely Kahler metrics. We establish its convergence on Kahler manifolds for suitable initial data. We also discuss its relation to some current problems in complex geometry.
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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.