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A parabolic approach to the Calabi-Yau problem in HKT geometry

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 نشر من قبل Luigi Vezzoni
 تاريخ النشر 2021
  مجال البحث
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We consider the natural generalization of the parabolic Monge-Amp`ere equation to HKT geometry. We prove that in the compact case the equation has always a short-time solution and when the hypercomplex manifold is locally flat and admits a hyperkahler metric, then the equation has a long-time solution whose normalization converges to a solution of the quaternionic Monge-Amp`ere equation introduced by Alesker and Verbitsky. The result gives an alternative proof of a theorem of Alesker.



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