In this talk, we shall establish some Cheeger-Gromov-Taylor type compactness theorems via modified Ricci curvature. Our compactness theorems generalize the classical compactness theorem by Cheeger, Gromov and Taylor [1] and improve the Myers type theorem via modified Ricci curvature by Limoncu [2].
References
[1] J. Cheeger, M. Gromov and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982), 15-53.
[2] M. Limoncu, Modifications of the Ricci tensor and applications, Arch. Math. (Basel) 95 (2010), 191-199.
© Homare Tadano.