[1] L. Ambrosio and P. Tilli: Topics on Analysis in Metric Spaces, Oxford Lecture Series in Mathematics and its Applications 25, Oxford University Press, Oxford, 2004.
[2] D. Amir and V.D. Milman: Unconditional and symmetric sets in n-dimensional normed spaces, Israel J. Math. 37 (1980), 3–20.
[3] D. Bakry and M. Ledoux: Sobolev inequalities and Myers’s diameter theorem for an abstract Markov generator, Duke Math. J. 85 (1996), 253–270.
[4] F. Barthe: Levels of concentration between exponential and Gaussian, Ann. Fac. Sci. Toulouse Math. (6) 10 (2001), 393–404.
[5] P. Be´rard and D. Meyer: Ine´galite´s isope´rime´triques et applications, Ann. Sci. E´ cole Norm. Supe´r. (4) 15(1982), 513–541.
[6] M. Berger: Encounter with a Geometer, Part II, Notices Amer. Math. Soc. 47 (2000), 326–340.
[7] J. Cheeger: A lower bound for the smallest eigenvalue of the Laplacian; in Problems in Analysis (Papers dedicated to Salomon Bochner, 1969), Princeton Univ. Press, Princeton, New Jersey, 1970, 195–199.
[8] J. Cheeger: Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal. 9 (1999), 428–517.
[9] S.Y. Cheng: Eigenvalue comparison theorems and its geometric applications, Math. Z. 143 (1975), 289– 297.
[10] M. Gromov: Metric Structures for Riemannian and Non-Riemannian Spaces, Progress in Mathematics 152, Birkha¨user Boston, Inc., Boston, MA, 1999. Based on the 1981 French original: Structures Me´triques des Varie´te´s Riemanniennes. With appendices by M. Katz, P. Pansu and S. Semmes. Translated from the French by Sean Michael Bates.
[11] M. Gromov and V.D. Milman: A topological application of the isoperimetric inequality, Amer. J. Math. 105 (1983), 843–854.
[12] S. Keith: A differentiable structure for metric measure spaces, Adv. Math. 183 (2004), 271–315.
[13] M. Ledoux: A remark on hypercontractivity and the concentration of measure phenomenon in a compact Riemannian manifold, Israel J. Math. 69 (1990), 361–370.
[14] M. Ledoux: Isoperimetry and Gaussian analysis; in Lectures on Probability Theory and Statistics, Ecole d’Ete´ de Probabilite´s de Saint-Flour XXIV–1994, Lecture Notes in Math. 1648, 165–294, Springer-Verlag, Berlin-Heidelberg, 1996.
[15] M. Ledoux: Concentration of measure and logarithmic Sobolev inequalities; in Seminaire de Probabilite´s XXXIII, Lecture Notes in Math. 1709, 120–216, Springer-Verlag, Berlin-Heidelberg, 1999.
[16] M. Ledoux: The Concentration of Measure Phenomenon, Math. Surveys Monogr. 89, Amer. Math. Soc., Providence, Rhode Island, 2001.
[17] M. Ledoux: Spectral gap, logarithmic Sobolev constant, and geometric bounds; in Eigenvalues of Lapla- cians and other geometric operators, Surv. Differ. Geom. 9 (2004), 219–240.
[18] M. Ledoux and M. Talagrand: Probability in Banach Spaces: Isoperimetry and Processes, Springer-Verlag, Berlin-Heidelberg, 1991.
[19] P. Li and S.-T. Yau: Estimates of eigenvalues of a compact Riemannian manifold; in Geometry of the Laplace operator, Proc. Sympos. Pure Math. 36, Amer. Math. Soc., Providence, Rhode Island, 1980, 205– 239.
[20] A. Lichnerowicz: Ge´ome´trie des groupes de transformations, Travaux et Recherches Mathe´matiques III, Dunod, Paris, 1958.
[21] E. Milman: On the role of convexity in isoperimetry, spectral gap and concentration, Invent. Math. 177 (2009), 1–43.
[22] S.B. Myers: Riemannian manifolds with positive mean curvature, Duke Math. J. 8 (1941), 401–404.
[23] A. Naor, Y. Rabani and A. Sinclair: Quasisymmetric embeddings, the observable diameter, and expansion properties of graphs, J. Funct. Anal. 227 (2005), 273–303.
[24] T. Shioya: Metric measure geometry, Gromov’s theory of convergence and concentration of metrics and measures, IRMA Lectures in Mathematics and Theoretical Physics 25, EMS Publishing House, Zu¨rich, 2016.
[25] C. Villani: Optimal transport, Old and new, Grundlehren der mathematischen Wissenschaften 338, Springer-Verlag, Berlin Heidelberg, 2009.
[26] D. Yang: Lower bound estimates of the first eigenvalue for compact manifolds with positive Ricci curvature, Pacific J. Math. 190 (1999), 383–398.