Scalar Curvature of Definable CAT-Spaces

Advances in Geometry

Volumn 3, Issue 1, 2003, Pages 23-43

  Bernig, Andreas ^a  

^a Institut fuür Mathematik   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347549536     PISSN: 1615715X     EISSN: None     Source Type: Journal    
DOI: 10.1515/advg.2003.003     Document Type: Article

References (23)

1. K. Bekka, D. Trotman, Sur les propriétés métriques des espaces stratifiés. Preprint 1995.
2. A. Bernig, Scalar curvature of definable Alexandrov spaces. Adv. Geom. 2 (2002), 29-55. MR 1 880 000 Zbl 01701491.
3. J. Bochnak, M. Coste, M.-F. Roy, Geometrie algébrique réelle. Springer 1987. MR 90b:14030 Zbl 0633.14016.
4. M. R. Bridson, A. Haefliger, Metric spaces of non-positive curvature. Springer 1999. MR 2000k:53038 Zbl 01385418.
5. L. Bröcker, M. Kuppe, Integral geometry of tame sets. Geom. Dedicata 82 (2000), 285-323. MR 2002e:53113 Zbl 01547916.
6. L. Brocker, M. Kuppe, W. Scheufler, Inner metric properties of 2-dimensional semi-algebraic sets.
7. Rev. Mat. Univ. Complut. Madrid 10 (1997), 51-78. MR 98m:53084 Zbl 0920.14030.
8. Y. Burago, M. Gromov, G. Perelman, A. D. Aleksandrov spaces with curvatures bounded below. Uspekhi Mat. Nauk 47 (1992), no. 2 (284), 3-51, 222. MR 93m:53035 Zbl 0802.53018.
9. J. Cheeger, W. Müller, On the curvature of piecewise flat spaces. Comm. Math. Phys. 92 (1984), 405-454.
10. M. Coste, An introduction to o-minimal geometry. University di Pisa, Dipartimento di Matematica 2000.
11. M. Coste, An introduction to semialgebraic geometry. University 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 0818.53091.
14. M. Goresky, R. MacPherson, Stratified Morse theory. Springer 1988. MR 90d:57039 Zbl 0639.14012.
15. M. Gromov, Metric structures for Riemannian and non-Riemannian spaces. Birkhauser 1999. MR 2000d:53065 Zbl 0953.53002.
16. M. Kuppe, Integralgeometrie Whitney-Stratifizierter Mengen. Dissertation Münster 1999. Eprint http://wwwmath.uni-muenster.de/u/broecker.
17. K. Kurdyka, G. Raby, Densite des ensembles sous-analytiques. Ann. Inst. Fourier (Grenoble) 39 (1989), 753-771. MR 90k:32026 Zbl 0673.32015.
18. T. L. Loi, Verdier and strict Thom stratifications in o-minimal structures. Illinois J. Math. 42 (1998), 347-356. MR 99c:32058 Zbl 0909.32008.
19. G. Perelman, Spaces with curvature bounded below. In: Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), 517-525.
20. R. Thom, Ensembles et morphismes stratifies. Bull. Amer. Math. Soc. 75 (1969), 240-284. MR 39 #970 Zbl 0197.20502.
21. L. van den Dries, Tame topology and o-minimal structures. Cambridge Univ. Press 1998. MR 99j:03001 Zbl 0953.03045.
22. L. van den Dries, C. Miller, Geometric categories and o-minimal structures. Duke Math. J. 84 (1996), 497-540. MR 97i:32008 Zbl 0889.03025.
23. H. Weyl, On the volume of tubes. Am. J. Math. 61 (1939), 461-472. Zbl 0021.35503.