This analysis reveals a new version of the mean curvature comparison theorem through extensions of the Bakry-Émery-Ricci tensor, indicating implications for geometry.
We consider generalizations of the drifted Laplacian and the Bakry-Émery-Ricci tensor, and we prove a version of the mean curvature comparison theorem. Consequently, we prove a Myers-type theorem and a generalization of the Cheeger-Gromoll splitting theorem.
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Mota et al. (2025) studied this question.
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