Bakry-Émery Ricci Curvature on Manifolds with Boundary

Kenneth Moore
2021
A classic result in the field of Riemannian Geometry is the Splitting Theorem of Cheeger and Gromoll. Since this result there have been numerous alternate versions under a variety of different conditions. Continuing in this vein, we prove structure results on manifolds with boundary components under m-Bakry-Émery Ricci curvature bounds. First we look at a generalization of Frankel's theorem [9], extrapolating on the work of Peterson and Wilhelm [25]. We then prove some related corollaries that
more » ... ere shown by Choe and Fraser [4]. Finally we generalize the splitting theorems of Sakurai [28], [29] for manifolds with boundary and a non-gradient vector field.
doi:10.7939/r3-8x7g-g239 fatcat:wroxw23fcjeczbxchkygeneyae