In this note, we prove that a non-compact Riemannian manifold M with non-negative Bakry-Émery Ricci curvature and compact minimal boundary ?M is the isometric product ∂M ×[0,∞), provided that the potential function is bounded from above and has non-negative derivatives at ∂M along inner normal directions.
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Received by the editors August 17, 2018, and, in revised form, October 2, 2018. 2010 Mathematics Subject Classification. Primary 53C20, 53C21. The author was partially supported by the Natural Science Research grant 17KJD110007 for Institutions of Higher Education of Jiangsu Province, China.
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