[1] Aubin, T.: Problèmes isopérimétriques et espaces de Sobolev. J. Differ. Geom. 11 (1976), 573-598 French. DOI 10.4310/jdg/1214433725 | MR 0448404 | Zbl 0371.46011

[2] Aubin, T.: Nonlinear Analysis on Manifolds. Monge-Ampère Equations. Grundlehren der Mathematischen Wissenschaften 252, Springer, New York (1982). DOI 10.1007/978-1-4612-5734-9 | MR 0681859 | Zbl 0512.53044

[3] Aubin, T.: Some Nonlinear Problems in Riemannian Geometry. Springer Monographs in Mathematics, Springer, Berlin (1998). DOI 10.1007/978-3-662-13006-3 | MR 1636569 | Zbl 0896.53003

[4] Bakry, D., Émery, M.: Hypercontractivité de semi-groupes de diffusion. C. R. Acad. Sci., Paris, Sér. I 299 (1984), 775-778 French. MR 0772092 | Zbl 0563.60068

[5] Bakry, D., Émery, M.: Diffusions hypercontractives. Séminaire de probabilités XIX 1983/84 Lecture Notes in Mathematics 1123, Springer, Berlin (1985), 177-206. DOI 10.1007/BFb0075847 | MR 0889476 | Zbl 0561.60080

[6] Caffarelli, L., Kohn, R., Nirenberg, L.: First order interpolation inequalities with weights. Compos. Math. 53 (1984), 259-275. MR 0768824 | Zbl 0563.46024

[7] Catrina, F., Wang, Z.-Q.: On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions. Commun. Pure Appl. Math. 54 (2001), 229-258. DOI 10.1002/1097-0312(200102)54:2<229::AID-CPA4>3.0.CO;2-I | MR 1794994 | Zbl 1072.35506

[8] Chavel, I.: Eigenvalues in Riemannian Geometry. Pure and Applied Mathematics 115, Academic Press, Orlando (1984). DOI 10.1016/S0079-8169(13)62888-3 | MR 0768584 | Zbl 0551.53001

[9] Carmo, M. do, Xia, C.: Ricci curvature and the topology of open manifolds. Math. Ann. 316 (2000), 319-400. DOI 10.1007/s002080050018 | MR 1741276 | Zbl 0958.53025

[10] Carmo, M. P. do, Xia, C.: Complete manifolds with non-negative Ricci curvature and the Caffarelli-Kohn-Nirenberg inequalities. Compos. Math. 140 (2004), 818-826. DOI 10.1112/S0010437X03000745 | MR 2041783 | Zbl 1066.53073

[11] Freitas, P., Mao, J., Salavessa, I.: Spherical symmetrization and the first eigenvalue of geodesic disks on manifolds. Calc. Var. Partial Differ. Equ. 51 (2014), 701-724. DOI 10.1007/s00526-013-0692-7 | MR 3268868 | Zbl 1302.35275

[12] Gray, A.: Tubes. Addison-Wesley Publishing Company, Redwood City (1990). DOI 10.1007/978-3-0348-7966-8 | MR 1044996 | Zbl 0692.53001

[13] Hardy, G. H., Littlewood, J.-E., Pólya, G.: Inequalities. Cambridge University Press, Cambridge (1952). MR 0046395 | Zbl 0047.05302

[14] Hebey, E.: Sobolev Spaces on Riemannian Manifolds. Lecture Notes in Mathematics 1635, Springer, Berlin (1996). DOI 10.1007/BFb0092907 | MR 1481970 | Zbl 0866.58068

[15] Katz, N. N., Kondo, K.: Generalized space forms. Trans. Am. Math. Soc. 354 (2002), 2279-2284. DOI 10.1090/S0002-9947-02-02966-5 | MR 1885652 | Zbl 0990.53032

[16] Kondo, K., Tanaka, M.: Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. I. Math. Ann. 351 (2011), 251-266. DOI 10.1007/s00208-010-0593-4 | MR 2836657 | Zbl 1243.53072

[17] Ledoux, M.: On manifolds with non-negative Ricci curvature and Sobolev inequalities. Commun. Anal. Geom. 7 (1999), 347-353. DOI 10.4310/CAG.1999.v7.n2.a7 | MR 1685586 | Zbl 0953.53025

[18] Lieb, E. H.: Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities. Ann. Math. (2) 118 (1983), 349-374. DOI 10.2307/2007032 | MR 0717827 | Zbl 0527.42011

[19] Lott, J.: Some geometric properties of the Bakry-Émery-Ricci tensor. Comment. Math. Helv. 78 (2003), 865-883. DOI 10.1007/s00014-003-0775-8 | MR 2016700 | Zbl 1038.53041

[20] Mao, J.: Open manifold with nonnegative Ricci curvature and collapsing volume. Kyushu J. Math. 66 (2012), 509-516. DOI 10.2206/kyushujm.66.509 | MR 3051351 | Zbl 1276.53045

[21] Mao, J.: Eigenvalue Estimation and Some Results on Finite Topological Type. Ph.D. Thesis, IST-UTL (2013).

[22] Mao, J.: Eigenvalue inequalities for the $p$-Laplacian on a Riemannian manifold and estimates for the heat kernel. J. Math. Pures Appl. (9) 101 (2014), 372-393. DOI 10.1016/j.matpur.2013.06.006 | MR 3168915 | Zbl 1285.58013

[23] Mao, J.: The Gagliardo-Nirenberg inequalities and manifolds with non-negative weighted Ricci curvature. Kyushu J. Math. 70 (2016), 29-46. DOI 10.2206/kyushujm.70.029 | MR 3444586 | Zbl 1342.53056

[24] Perelman, G.: The entropy formula for the Ricci flow and its geometric applications. Available at https://arxiv.org/abs/math/0211159 (2002). Zbl 1130.53001

[25] Petersen, P.: Comparison geometry problem list. Riemannian Geometry Fields Institute Monographs 4, American Mathematical Society, Providence (1996), 87-115. DOI 10.1090/fim/004/04 | MR 1377310 | Zbl 0843.53031

[26] Schoen, R., Yau, S.-T.: Lectures on Differential Geometry. Conference Proceedings and Lecture Notes in Geometry and Topology 1, International Press, Cambridge (1994). MR 1333601 | Zbl 0830.53001

[27] Shiohama, K., Tanaka, M.: Compactification and maximal diameter theorem for noncompact manifolds with radial curvature bounded below. Math. Z. 241 (2002), 341-351. DOI 10.1007/s002090200418 | MR 1935490 | Zbl 1020.53019

[28] Talenti, G.: Best constant in Sobolev inequality. Ann. Mat. Pura Appl. (4) 110 (1976), 353-372. DOI 10.1007/BF02418013 | MR 0463908 | Zbl 0353.46018

[29] Wei, G., Wylie, W.: Comparison geometry for the Bakry-Emery Ricci tensor. J. Differ. Geom. 83 (2009), 377-405. DOI 10.4310/jdg/1261495336 | MR 2577473 | Zbl 1189.53036

[30] Xia, C.: Complete manifolds with nonnegative Ricci curvature and almost best Sobolev constant. Ill. J. Math. 45 (2001), 1253-1259. DOI 10.1215/ijm/1258138064 | MR 1894894 | Zbl 0996.53024

[31] Xia, C.: The Gagliardo-Nirenberg inequalities and manifolds of non-negative Ricci curvature. J. Funct. Anal. 224 (2005), 230-241. DOI 10.1016/j.jfa.2004.11.009 | MR 2139111 | Zbl 1071.53019

[32] Xia, C.: The Caffarelli-Kohn-Nirenberg inequalities on complete manifolds. Math. Res. Lett. 14 (2007), 875-885. DOI 10.4310/MRL.2007.v14.n5.a14 | MR 2350131 | Zbl 1143.53036