We prove certain gradient and eigenvalue estimates, as well as the heat kernel estimates, for the Hodge Laplacian on (m, 0) forms, i.e., sections of the canonical bundle of Kähler manifolds, where m is the complex dimension of the manifold. Instead of the usual dependence on curvature tensor, our condition depends only on the Ricci curvature bound. The proof is based on a new Bochner type formula for the gradient of (m, 0) forms, which involves only the Ricci curvature and the gradient of the scalar curvature.

中文翻译：

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Kähler流形规范束上的梯度和特征值估计

我们证明了（m，0）形式上的Hodge Laplacian的某些梯度和特征值估计以及热核估计，即Kähler流形的标准束的截面，其中m是流形的复数维。而不是通常依赖于曲率张量，我们的条件仅取决于Ricci曲率边界。该证明基于（m，0）形式的梯度的新Bochner类型公式，该公式仅涉及Ricci曲率和标量曲率的梯度。