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arXiv · 2310.09225

The parabolic quaternionic Monge-Amp\`{e}re type equation on hyperK\"{a}hler manifolds

Jixiang Fu·Xin Xu·Dekai Zhang
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Abstract

We prove the long time existence and uniqueness of solution to a parabolic quaternionic Monge-Amp\`{e}re type equation on a compact hyperK\"{a}hler manifold. We also show that after normalization, the solution converges smoothly to the unique solution of the Monge-Amp\`{e}re equation for $(n-1)$-quaternionic psh functions.

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Jixiang Fu, Xin Xu, Dekai Zhang. 2023-10-13. The parabolic quaternionic Monge-Amp\`{e}re type equation on hyperK\"{a}hler manifolds. https://arxiv.org/abs/2310.09225

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