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
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
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, DOI 10.1090/conm/338
André Bellaïche and Jean-Jacques Risler (eds.), Sub-Riemannian geometry, Progress in Mathematics, vol. 144, Birkhäuser Verlag, Basel, 1996. MR 1421821, DOI 10.1007/978-3-0348-9210-0
J. W. S. Cassels, Local fields, London Mathematical Society Student Texts, vol. 3, Cambridge University Press, Cambridge, 1986. MR 861410, DOI 10.1017/CBO9781139171885
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
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, DOI 10.1090/S0002-9904-1977-14325-5
Fernando Q. Gouvêa, $p$-adic numbers, 2nd ed., Universitext, Springer-Verlag, Berlin, 1997. An introduction. MR 1488696, DOI 10.1007/978-3-642-59058-0
Juha Heinonen, Calculus on Carnot groups, Fall School in Analysis (Jyväskylä, 1994) Report, vol. 68, Univ. Jyväskylä, Jyväskylä, 1995, pp. 1–31. MR 1351042, DOI 10.1530/jrf.0.0680001
Juha Heinonen, Lectures on analysis on metric spaces, Universitext, Springer-Verlag, New York, 2001. MR 1800917, DOI 10.1007/978-1-4613-0131-8
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
Jun Kigami, Analysis on fractals, Cambridge Tracts in Mathematics, vol. 143, Cambridge University Press, Cambridge, 2001. MR 1840042, DOI 10.1017/CBO9780511470943
Steven G. Krantz, Complex analysis: the geometric viewpoint, 2nd ed., Carus Mathematical Monographs, vol. 23, Mathematical Association of America, Washington, DC, 2004. MR 2047863, DOI 10.5948/UPO9780883859681
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, DOI 10.1090/surv/091
Stephen Semmes, An introduction to analysis on metric spaces, Notices Amer. Math. Soc. 50 (2003), no. 4, 438–443. MR 1960309
Stephen Semmes, An introduction to Heisenberg groups in analysis and geometry, Notices Amer. Math. Soc. 50 (2003), no. 6, 640–646. MR 1988576
Stephen Semmes, Happy fractals and some aspects of analysis on metric spaces, Publ. Mat. 47 (2003), no. 2, 261–309. MR 2006486, DOI 10.5565/PUBLMAT_{4}7203_{0}1
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
Robert S. Strichartz, Analysis on fractals, Notices Amer. Math. Soc. 46 (1999), no. 10, 1199–1208. MR 1715511
M. H. Taibleson, Fourier analysis on local fields, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. MR 0487295
A. C. Thompson, Minkowski geometry, Encyclopedia of Mathematics and its Applications, vol. 63, Cambridge University Press, Cambridge, 1996. MR 1406315, DOI 10.1017/CBO9781107325845
Edoardo Vesentini, Invariant metrics on convex cones, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), no. 4, 671–696. MR 433228
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
- 1.
- L. Ambrosio and P. Tilli, Topics on Analysis in Metric Spaces, Oxford University Press, 2004. MR 2039660
- 2.
- P. Auscher, T. Coulhon, and A. Grigoryan, editors, Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces, American Mathematical Society, 2003. MR 2041910
- 3.
- A. Bellaïche and J.-J. Risler, editors, Sub-Riemannian Geometry, Birkhäuser, 1996. MR 1421821
- 4.
- J. Cassels, Local Fields, Cambridge University Press, 1986. MR 0861410
- 5.
- R. Coifman and G. Weiss, Analyse Harmonique Non-Commutative sur Certains Espaces Homogènes, Lecture Notes in Mathematics 242, Springer-Verlag, 1971. MR 0499948
- 6.
- R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. MR 0447954
- 7.
- F. Gouvêa,
-Adic Numbers: An Introduction, 2nd edition, Springer-Verlag, 1997. MR 1488696
- 8.
- J. Heinonen, Calculus on Carnot groups, in Fall School in Analysis, 1-31, Reports of the Department of Mathematics and Statistics 68, University of Jyväskylä, 1995. MR 1351042
- 9.
- J. Heinonen, Lectures on Analysis on Metric Spaces, Springer-Verlag, 2001. MR 1800917
- 10.
- J. Heinonen, Geometric embeddings of metric spaces, Reports of the Department of Mathematics and Statistics 90, University of Jyväskylä, 2003. MR 2014506
- 11.
- J. Kigami, Analysis on Fractals, Cambridge University Press, 2001. MR 1840042
- 12.
- S. Krantz, Complex Analysis: The Geometric Viewpoint, 2nd edition, Mathematical Association of America, 2004. MR 2047863
- 13.
- R. Montgomery, A Tour of Subriemannian Geometries, Their Geodesics and Applications, American Mathematical Society, 2002. MR 1867362
- 14.
- S. Semmes, An introduction to analysis on metric spaces, Notices Amer. Math. Soc. 50 (2003), 438-443. MR 1960309
- 15.
- S. Semmes, An introduction to Heisenberg groups in analysis and geometry, Notices Amer. Math. Soc. 50 (2003), 640-646. MR 1988576
- 16.
- S. Semmes, Happy fractals and some aspects of analysis on metric spaces, Publ. Mat. 47 (2003), 261-309. MR 2006486
- 17.
- E. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, with the assistance of T. Murphy, Princeton University Press, 1993. MR 1232192
- 18.
- R. Strichartz, Analysis on fractals, Notices Amer. Math. Soc. 46 (1999), 1199-1208. MR 1715511
- 19.
- M. Taibleson, Fourier Analysis on Local Fields, Princeton University Press, 1975. MR 0487295
- 20.
- A. Thompson, Minkowski Geometry, Cambridge University Press, 1996. MR 1406315
- 21.
- E. Vesentini, Invariant metrics on convex cones, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), 671-696. MR 0433228
- 22.
- N. Varopoulos, L. Saloff-Coste, and T. Coulhon, Analysis and Geometry on Groups, Cambridge University Press, 1992. MR 1218884
Review Information:
Reviewer:
Stephen Semmes
Affiliation:
Rice University
Email:
semmes@rice.edu
Journal:
Bull. Amer. Math. Soc.
43 (2006), 435-438
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.
