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<p>In this paper, we study a class of complex Hessian equations with left-hand sides depending on gradients on Hermitian manifolds and derive a priori second order estimates for admissible solutions. This form of estimates shares a similar form to the one developed by Hou–Ma–Wu on Kähler manifolds and can be applied to blowup analysis.</p>

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A priori estimates for a class of complex Hessian equations on Hermitian manifolds

  • 期刊论文

  • 发表日期：

    2025年10月21日

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  • Pang Xu,
  • Xin-An Ren

摘要

In this paper, we study a class of complex Hessian equations with left-hand sides depending on gradients on Hermitian manifolds and derive a priori second order estimates for admissible solutions. This form of estimates shares a similar form to the one developed by Hou–Ma–Wu on Kähler manifolds and can be applied to blowup analysis.