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Book Review

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Book Information:

Author: Athanase Papadopoulos
Title: Metric spaces, convexity, and nonpositive curvature
Additional book information: European Math. Soc., Zürich, 2005, xii + 287 pp., ISBN 3-03719-010-8, EUR 48.00

1. Luigi Ambrosio and Paolo Tilli, Topics on analysis in metric spaces, Oxford Lecture Series in Mathematics and its Applications, vol. 25, Oxford University Press, Oxford, 2004. MR 2039660
2. Pascal Auscher, Thierry Coulhon, and Alexander Grigor’yan (eds.), Heat kernels and analysis on manifolds, graphs, and metric spaces, Contemporary Mathematics, vol. 338, American Mathematical Society, Providence, RI, 2003. Lecture notes from a Quarter Program on Heat Kernels, Random Walks, and Analysis on Manifolds and Graphs held in Paris, April 16–July 13, 2002. MR 2041910
3. André Bellaïche and Jean-Jacques Risler (eds.), Sub-Riemannian geometry, Progress in Mathematics, vol. 144, Birkhäuser Verlag, Basel, 1996. MR 1421821
4. J. W. S. Cassels, Local fields, London Mathematical Society Student Texts, vol. 3, Cambridge University Press, Cambridge, 1986. MR 861410
5. Ronald R. Coifman and Guido Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Mathematics, Vol. 242, Springer-Verlag, Berlin-New York, 1971 (French). Étude de certaines intégrales singulières. MR 0499948
6. Ronald R. Coifman and Guido Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569–645. MR 447954, https://doi.org/10.1090/S0002-9904-1977-14325-5
7. Fernando Q. Gouvêa, 𝑝-adic numbers, 2nd ed., Universitext, Springer-Verlag, Berlin, 1997. An introduction. MR 1488696
8. Juha Heinonen, Calculus on Carnot groups, Fall School in Analysis (Jyväskylä, 1994) Report, vol. 68, Univ. Jyväskylä, Jyväskylä, 1995, pp. 1–31. MR 1351042, https://doi.org/10.1530/jrf.0.0680001
9. Juha Heinonen, Lectures on analysis on metric spaces, Universitext, Springer-Verlag, New York, 2001. MR 1800917
10. Juha Heinonen, Geometric embeddings of metric spaces, Report. University of Jyväskylä Department of Mathematics and Statistics, vol. 90, University of Jyväskylä, Jyväskylä, 2003. MR 2014506
11. Jun Kigami, Analysis on fractals, Cambridge Tracts in Mathematics, vol. 143, Cambridge University Press, Cambridge, 2001. MR 1840042
12. Steven G. Krantz, Complex analysis: the geometric viewpoint, 2nd ed., Carus Mathematical Monographs, vol. 23, Mathematical Association of America, Washington, DC, 2004. MR 2047863
13. Richard Montgomery, A tour of subriemannian geometries, their geodesics and applications, Mathematical Surveys and Monographs, vol. 91, American Mathematical Society, Providence, RI, 2002. MR 1867362
14. Stephen Semmes, An introduction to analysis on metric spaces, Notices Amer. Math. Soc. 50 (2003), no. 4, 438–443. MR 1960309
15. Stephen Semmes, An introduction to Heisenberg groups in analysis and geometry, Notices Amer. Math. Soc. 50 (2003), no. 6, 640–646. MR 1988576
16. Stephen Semmes, Happy fractals and some aspects of analysis on metric spaces, Publ. Mat. 47 (2003), no. 2, 261–309. MR 2006486, https://doi.org/10.5565/PUBLMAT_47203_01
17. Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
18. Robert S. Strichartz, Analysis on fractals, Notices Amer. Math. Soc. 46 (1999), no. 10, 1199–1208. MR 1715511
19. M. H. Taibleson, Fourier analysis on local fields, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. MR 0487295
20. A. C. Thompson, Minkowski geometry, Encyclopedia of Mathematics and its Applications, vol. 63, Cambridge University Press, Cambridge, 1996. MR 1406315
21. Edoardo Vesentini, Invariant metrics on convex cones, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), no. 4, 671–696. MR 433228
22. N. Th. Varopoulos, L. Saloff-Coste, and T. Coulhon, Analysis and geometry on groups, Cambridge Tracts in Mathematics, vol. 100, Cambridge University Press, Cambridge, 1992. MR 1218884

Review Information:

Reviewer: Stephen Semmes
Affiliation: Rice University
Email: semmes@rice.edu

Journal: Bull. Amer. Math. Soc. 43 (2006), 435-438
MSC (2000): Primary 51-02, 52-02, 53-02
Published electronically: April 19, 2006
Review copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.