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<p>This paper proves the long-time existence and uniqueness of solutions to a parabolic quaternionic Monge-Ampère type equation on compact hyperKähler manifolds. Moreover, it is shown that after normalization, the solution converges smoothly to the unique solution of the Monge-Ampère equation for (<i>n</i> − 1)-quaternionic psh functions.</p>

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The Parabolic Quaternionic Monge-Ampère Type Equation on HyperKähler Manifolds

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Jixiang Fu,
  • Xin Xu,
  • Dekai Zhang

摘要

This paper proves the long-time existence and uniqueness of solutions to a parabolic quaternionic Monge-Ampère type equation on compact hyperKähler manifolds. Moreover, it is shown that after normalization, the solution converges smoothly to the unique solution of the Monge-Ampère equation for (n − 1)-quaternionic psh functions.