“…Motivated by unified string theories and mirror symmetry, there has recently been interest in extending the theory of such equations beyond the Kähler setting to more general classes of Hermitian manifolds [27,24,17,10,12,13,14,19,20,26,2,11].…”
We prove the long-time existence and convergence of a general class of parabolic equations, not necessarily concave in the Hessian of the unknown function, on a compact Hermitian manifold. The limiting function is identified as the solution of an elliptic complex Monge-Ampère equation.
“…Motivated by unified string theories and mirror symmetry, there has recently been interest in extending the theory of such equations beyond the Kähler setting to more general classes of Hermitian manifolds [27,24,17,10,12,13,14,19,20,26,2,11].…”
We prove the long-time existence and convergence of a general class of parabolic equations, not necessarily concave in the Hessian of the unknown function, on a compact Hermitian manifold. The limiting function is identified as the solution of an elliptic complex Monge-Ampère equation.
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