We study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition, and a suitable condition for the weighted mean curvature for the boundary, we obtain various comparison geometric results.

中文翻译：

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具有较低权重 RICCI 曲率边界下的流形与边界的比较几何

我们研究了在较低加权 Ricci 曲率边界下具有边界的黎曼流形。我们考虑一种曲率条件，其中加权 Ricci 曲率由密度函数从下方限定。在曲率条件下，以及边界加权平均曲率的合适条件下，我们得到了各种比较几何结果。