L^∞ estimate for the potential of quaternionic Gauduchon metric with prescribed volume form
arxiv（2023）
摘要
Quaternionic Calabi conjecture was raised by Alesker and Verbitsky
, it predicts that one can solve the
quaternionic Monge-Ampère equation on any compact HKT manifold. Motivated by
this conjecture a quaternionic version of Gauduchon conjecture on any compact
SL(n,)̋-manifold will be introduced, namely the existence of quaternionic
Gauduchon metrics with prescribed volume form. We reformulate this question
into a special case of fully nonlinear elliptic equations of second order, and
the L^∞ estimate for the potential function will be established.
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