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Title: Compactness theorems for the Bakry-Emery Ricci tensor on semi-Riemannian manifolds (English)
Author: Santos, M. S.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 58
Issue: 1
Year: 2017
Pages: 79-86
Summary lang: English
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Category: math
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Summary: In this manuscript we provide new extensions for the Myers theorem in weighted Riemannian and Lorentzian manifolds. As application we obtain a closure theorem for spatial hypersurfaces immersed in some time-like manifolds. (English)
Keyword: Bakry-Emery Ricci curvature tensor
Keyword: closure theorem
Keyword: Riccati equation
MSC: 53C20
idZBL: Zbl 06736745
idMR: MR3631682
DOI: 10.14712/1213-7243.2015.177
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Date available: 2017-03-12T16:40:09Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/146029
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Reference: [1] Bakry D., Emery E.: Diffusions hypercontractives.Séminaire de probabilités, XIX, 1983/84, Lecture Notes in Math., 1123, Springer, Berlin, 1985, pp. 177–206. Zbl 0561.60080, MR 0889476
Reference: [2] Bakry D., Ledoux M.: Sobolev inequalities and Myers diameter theorem for an abstract Markov generator.Duke Math. J. 81 (1996), no. 1, 252–270. MR 1412446
Reference: [3] Beem J., Ehrlich P., Easley K.: Global Lorentzian Geometry.2nd edn., Marcel Dekker, New York, 1996. Zbl 0846.53001, MR 1384756
Reference: [4] Case J.: Singularity theorems and the lorentzian splitting theorem for the Bakry-Emery-Ricci tensor.J. Geom. Phys. 60 (2010), no. 3, 477–490. Zbl 1188.53075, MR 2600009, 10.1016/j.geomphys.2009.11.001
Reference: [5] Cavalcante M.P., Oliveira J.Q., Santos M.S.: Compactness in weighted manifolds and applications.Results Math. 68 (2015), 143–156. Zbl 1327.53037, MR 3391497, 10.1007/s00025-014-0427-x
Reference: [6] Frankel T.: Gravitation Curvature. An Introduction to Einstein's Theory.W.H. Freeman and Co., San Francisco, Calif., 1979. MR 0518868
Reference: [7] Frankel T., Galloway G.: Energy density and spatial curvature in general relativity.J. Math. Phys. 22 (1981), no. 4, 813–817. Zbl 0483.76135, MR 0617327, 10.1063/1.524961
Reference: [8] Galloway G.J.: A generalization of Myers theorem and an application to relativistic cosmology.J. Differential Geom. 14 (1979), 105–116. Zbl 0444.53036, MR 0577883, 10.4310/jdg/1214434856
Reference: [9] Galloway G.J., Woolgar E.: Cosmological singularities in Bakry-Émery space-times.preprint, 2013. MR 3282334
Reference: [10] Ledoux M.: The geometry of Markov diffusion generators.Ann. Fac. Sci. Toulouse Math. 9 (2000), no. 2, 305–366. Zbl 0980.60097, MR 1813804, 10.5802/afst.962
Reference: [11] Limoncu M.: The Bakry-Emery Ricci tensor and its applications to some compactness theorems.Math. Z. 271 (2012), 715–722. Zbl 1264.53042, MR 2945580, 10.1007/s00209-011-0886-7
Reference: [12] Limoncu M.: Modifications of the Ricci tensor and applications.Arch. Math. (Basel) 95 (2010), 191–199. MR 2674255, 10.1007/s00013-010-0150-0
Reference: [13] Lott J.: Some geometric properties of the Bakry-Émery-Ricci tensor.Comment. Math. Helv. 78 (2003), no. 4, 865–883. Zbl 1038.53041, MR 2016700, 10.1007/s00014-003-0775-8
Reference: [14] Morgan F.: Myers' theorem with density.Kodai Math. J. 29 (2006), no. 3, 454–461. Zbl 1132.53306, MR 2278776, 10.2996/kmj/1162478772
Reference: [15] Myers S.B.: Riemannian manifolds with positive mean curvature.Duke Math. J. 8 (1941) 401–404. Zbl 0025.22704, MR 0004518, 10.1215/S0012-7094-41-00832-3
Reference: [16] Qian Z.: Estimates for weighted volumes and applications.Quart. J. Math. Oxford 48 (1997), 235–242. Zbl 0902.53032, MR 1458581, 10.1093/qmath/48.2.235
Reference: [17] Rimoldi M.: A remark on Einstein warped products.Pacific J. Math. 252 (2011), no. 1, 207–218. Zbl 1232.53036, MR 2862148, 10.2140/pjm.2011.252.207
Reference: [18] Ringström H.: On the Topology and Future Stability of the Universe.Oxford Mathematical Monographs, Oxford University Press, Oxford, 2013. Zbl 1270.83005, MR 3186493
Reference: [19] Rupert M., Woolgar E.: Bakry-Émery black holes.Classical Quantum Gravity 31 (2014), no. 2, 025008. Zbl 1302.83023, MR 3157702, 10.1088/0264-9381/31/2/025008
Reference: [20] Sprouse S.: Integral curvature bounds and bounded diameter.Comm. Anal. Geom. 8 (2000), 531–543. Zbl 0984.53018, MR 1775137, 10.4310/CAG.2000.v8.n3.a4
Reference: [21] Wei G., Wylie W.: Comparison geometry for the Bakry-Emery Ricci tensor.J. Differential Geom. 83 (2009), no. 2, 377–405. Zbl 1189.53036, MR 2577473
Reference: [22] Woolgar E.: Scalar-tensor gravitation and the Bakry-Emery-Ricci tensor.Classical Quantum Gravity 30 (2013) 085007. Zbl 1267.83094, MR 3044364, 10.1088/0264-9381/30/8/085007
Reference: [23] Yun J.-G.: A note on the generalized Myers theorem.Bull. Korean Math. Soc. 46 (2009), no. 1, 61–66. Zbl 1176.53045, MR 2488500, 10.4134/BKMS.2009.46.1.061
Reference: [24] Zhang S.: A theorem of Ambrose for Bakry-Emery Ricci tensor.Ann. Global Anal. Geom. 45 (2014), no. 3, 233–238. Zbl 1292.53027, MR 3170524, 10.1007/s10455-013-9396-7
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