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.
T-dual solutions of the Hull-Strominger system on non-K\"ahler threefolds
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abstract
We construct new examples of solutions of the Hull-Strominger system on non-K\"ahler torus bundles over K3 surfaces, with the property that the connection $\nabla$ on the tangent bundle is Hermite-Yang-Mills. With this ansatz for the connection $\nabla$, we show that the existence of solutions reduces to known results about moduli spaces of slope-stable sheaves on a K3 surface, combined with elementary analytical methods. We apply our construction to find the first examples of T-dual solutions of the Hull-Strominger system on compact non-K\"ahler manifolds with different topology.
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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.