참고문헌
- U. Abresch and D. Gromoll, On complete manifolds with nonnegative Ricci curvature, J. Amer. Math. Soc. 3 (1990), no. 2, 355-374. https://doi.org/10.2307/1990957
- J. Cheeger and T. H. Colding, Almost rigidity of warped products and the structure of spaces with Ricci curvature bounded below, C. R. Acad. Sci. Paris Ser. I Math. 320 (1995), no. 3, 353-357.
- J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geometry 6 (1971/72), 119-128. http://projecteuclid.org/euclid.jdg/1214430220
- T. H. Colding, Large manifolds with positive Ricci curvature, Invent. Math. 124 (1996), no. 1-3, 193-214. https://doi.org/10.1007/s002220050050
- K. Grove and P. Petersen, Comparison Geometry, Mathematical Sciences Research Institute Publications, 30, Cambridge University Press, Cambridge, 1997.
- X. Hu, D. Ji, and Y. Shi, Volume comparison of conformally compact manifolds with scalar curvature R ≥ -n(n - 1), Ann. Henri Poincare 17 (2016), no. 4, 953-977. https://doi.org/10.1007/s00023-015-0411-3
- J. Lott, Some geometric properties of the Bakry-Emery-Ricci tensor, Comment. Math. Helv. 78 (2003), no. 4, 865-883. https://doi.org/10.1007/s00014-003-0775-8
- P. Petersen and G. Wei, Relative volume comparison with integral curvature bounds, Geom. Funct. Anal. 7 (1997), no. 6, 1031-1045. https://doi.org/10.1007/s000390050036
- Z. Qian, Estimates for weighted volumes and applications, Quart. J. Math. Oxford Ser. (2) 48 (1997), no. 190, 235-242. https://doi.org/10.1093/qmath/48.2.235
- G. Wei, Examples of complete manifolds of positive Ricci curvature with nilpotent isometry groups, Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 1, 311-313. https://doi.org/10.1090/S0273-0979-1988-15653-4
- G. Wei and W. Wylie, Comparison geometry for the Bakry-Emery Ricci tensor, J. Differential Geom. 83 (2009), no. 2, 377-405. https://doi.org/10.4310/jdg/1261495336
- N. Yang, A note on nonnegative Bakry-Emery Ricci curvature, Arch. Math. (Basel) 93 (2009), no. 5, 491-496. https://doi.org/10.1007/s00013-009-0062-z
- W. Yuan, Volume comparison with respect to scalar curvature, Math. DG (2021).
- Q. S. Zhang and M. Zhu, New volume comparison results and applications to degeneration of Riemannian metrics, Adv. Math. 352 (2019), 1096-1154. https://doi.org/10.1016/j.aim.2019.06.030
- S. Zhu, The comparison geometry of Ricci curvature, in Comparison geometry (Berkeley, CA, 1993-94), 221-262, Math. Sci. Res. Inst. Publ., 30, Cambridge Univ. Press, Cambridge, 1997.