Scalar curvature of definable Alexandrov spaces

Advances in Geometry

Volumn 2, Issue 1, 2002, Pages 29-55

  Bernig, Andreas ^a  

^a SFB 478 Geometrische Strukturen in der Mathematik ^*  (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011573419     PISSN: 1615715X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. K. Bekka, D. Trotman, Sur les propriétés métriques des espaces stratiés. Preprint 1995.
2. J. Bochnak, M. Coste, M.-F. Roy, Géométrie algébrique réelle. Springer 1987. MR 90b:14030 Zbl 633.14016
3. M. R. Bridson, A. Haefliger, Metric spaces of non-positive curvature. Springer 1999. MR 2000k:5303S Zbl 991.00075
4. L. Bröcker, M. Kuppe, Integral geometry of tame sets. Geom. Dedicata 82 (2000), 285-323. MR 1 789 065 Zbl 992.10298
5. L. Bröcker, M. Kuppe, W. Scheufler, Inner metric properties of 2-dimensional semialgebraic sets. Rev. Mat. Univ. Complut. Madrid 10 (1997), 51-78. MR 98m:53084 Zbl 920.14030
6. Y. Burago, M. Gromov, G. Perel'man, A. D. Aleksandrov spaces with curvatures bounded below. Russ. Math. Surv. 47 (1992), 1-58. MR 93m:53035 Zbl 802.53018
7. J. Cheeger, W. Müller, R. Schrader, On the curvature of piecewise flat spaces. Comm. Math. Phys. 92 (1984), 405-454. MR 85m:53037 Zbl 559.53028
8. J. Cheeger, W. Müller, R. Schrader, Kinematic and tube formulas for piecewise linear spaces. Indiana Univ. Math. J. 35 (1986), 737-754. MR 87m:53083 Zbl 615.53058
9. G. Comte, Densité et images polaires en géométrie sous-analytiques. Thèse de doctorat, Université de Provence 1998.
10. M. Coste, An introduction to o-minimal geometry. Università di Pisa, Dipartimento di Matematica 2000.
11. M. Coste, An introduction to semialgebraic geometry. Universitá di Pisa, Dipartimento di Matematica 2000.
12. M. Ferrarotti, About geodesic distance on Riemannian stratified spaces. Preprint 1997.
13. J. H. G. Fu, Curvature measures of subanalytic sets. Amer. J. Math. 116 (1994), 819-880. MR 95g:32016 Zbl 818.53091
14. M. Goresky, R. MacPherson, Stratified Morse theory. Springer 1988. MR 90d:57039 Zbl 639.14012
15. M. Gromov, Metric structures for Riemannian and non-Riemannian spaces. Birkhäuser 1999. MR 2000d:53065 Zbl 953.53002
16. M. Kuppe, Integralgeometrie Whitney-stratifizierter Mengen. Dissertation Münster 1999. http://www.math.uni-muenster.de/u/broecker Zbl 946.53041
17. K. Kurdyka, G. Raby, Densité des ensembles sous-analytiques. Ann. Inst. Fourier (Grenoble) 39 (1989), 753-771. MR 90k:32026 Zbl 673.32015
18. T. L. Loi, Verdier and strict Thom stratifications in o-minimal structures. Illinois J. Math. 42 (1998), 347-356. MR 99c:3205S Zbl 909.32008
19. A. Parusiński, Lipschitz stratification of subanalytic sets. Ann. Sci. École Norm. Sup. (4) 27 (1994), 661-696. MR 96g:32017 Zbl 819.32007
20. G. Perelman, Spaces with curvature bounded below. In: Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), 517-525, Birkhäuser 1995. MR 97g:53055 Zbl 838.53033
21. Z. M. Shen, A regularity theorem for Alexandrov spaces. Math. Nachr. 164 (1993), 91-102. MR 94j:53054 Zbl 815.53071
22. L. van den Dries, Tame topology and o-minimal structures. Cambridge Univ. Press 1998. MR 99j:03001 Zbl 953.03045
23. L. van den Dries, C. Miller, Geometric categories and o-minimal structures. Duke Math. J. 84 (1996), 497-540. MR 97i:32008 Zbl 889.03025
24. H. Weyl, On the volume of tubes. Amer. J. Math. 61 (1939), 461-472. Zbl 021.35503