论文标题
梯度和特征值估算的Kähler歧管捆绑
Gradient and Eigenvalue Estimates on the canonical bundle of Kähler manifolds
论文作者
论文摘要
我们证明了hodge laplacian的某些梯度和特征值估计以及热内核的估计值（m，0）$形式，即$ m $是$ m $的典范捆绑包的部分。我们的状况仅取决于RICCI曲率结合，而不是通常对曲率张量的依赖性。该证明基于$（m，0）$表单的梯度的新型Bochner类型公式，该公式仅涉及RICCI曲率和标量曲率的梯度。
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.
