Inserted: 27 sep 2017
Last Updated: 28 sep 2017
This is my preliminary attempt to study metric measure space with boundary.
The aim of this note is to study the measure-valued Ricci tensor on smooth metric measure space with boundary, which is a generalization of Bakry-Emery's modified Ricci tensor on weighted Riemannian manifold. As an application, we offer a new approach to study curvature-dimension condition of smooth metric measure space with boundary.