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arXiv · 1607.02608

The parabolic Monge-Amp\`ere equation on compact almost Hermitian manifolds

Jianchun Chu
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Abstract

We prove the long time existence and uniqueness of solutions to the parabolic Monge-Amp\`ere equation on compact almost Hermitian manifolds. We also show that the normalization of solution converges to a smooth function in $C^{\infty}$ topology as $t\rightarrow\infty$. Up to scaling, the limit function is a solution of the Monge-Amp\`ere equation. This gives a parabolic proof of existence of solutions to the Monge-Amp\`ere equation on almost Hermitian manifolds.

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Jianchun Chu. 2016-07-09. The parabolic Monge-Amp\`ere equation on compact almost Hermitian manifolds. https://arxiv.org/abs/1607.02608

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