In this paper, under m-Bakry–Émery (or \(\infty \)-Bakry–Émery) pseudohermitian Ricci curvature condition, we derive subgradient estimate for positive solutions of \(\Delta _{H,\phi } u(x)=-\lambda u(x)\) on a weighted complete noncompact pseudohermitian manifold which satisfies the sub-Laplacian comparison property.

中文翻译：

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Witten次拉普拉斯算子正本征函数的CR梯度估计

在本文中，在m -Bakry–Émery（或\（\ infty \）- Bakry–Émery）伪厄密Ricci曲率条件下，我们得出\（\ Delta _ {H，\ phi} u（x ）=-\ lambda u（x）\）在满足sub-Laplacian比较性质的加权完全非紧致伪厄密流形上。