Mesures de courbure des variétés lisses et des polyèdres
Séminaire Bourbaki : volume 1985/86, exposés 651-668, Astérisque, no. 145-146 (1987), Talk no. 664, p. 241-256
@incollection{SB_1985-1986__28__241_0,
     author = {Lafontaine, Jacques},
     title = {Mesures de courbure des vari\'et\'es lisses et des poly\`edres},
     booktitle = {S\'eminaire Bourbaki : volume 1985/86, expos\'es 651-668},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {145-146},
     year = {1987},
     note = {talk:664},
     pages = {241-256},
     zbl = {0613.53031},
     mrnumber = {880036},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1985-1986__28__241_0}
}
Lafontaine, Jacques. Mesures de courbure des variétés lisses et des polyèdres, in Séminaire Bourbaki : volume 1985/86, exposés 651-668, Astérisque, no. 145-146 (1987), Talk no. 664, pp. 241-256. http://www.numdam.org/item/SB_1985-1986__28__241_0/

[A-W] C. Allendoerfer and A. Weil - The Gauss - Bonnet theorem for Riemannian polyhedra, Trans. Amer. Math. Soc. VI, 53, 101-129. | MR 7627 | Zbl 0060.38102

[A] M. F. Atiyah - The Heat Equation in Riemannian Geometry, after Patodi, Gilkey, etc., Sém. Bourbaki 1973/74, exposé n° 436, Springer-Verlag, Lect. Notes in Math. 431(1975), 1-11. | Numdam | MR 431286 | Zbl 0322.58011

[A-B-P] M. F. Attyah, R. Bott and V. K. Patodi - On the Heat Equation and the Index Theonem, Inv. Math 19 (1973), 279-330. | MR 650828 | Zbl 0257.58008

[Ba] T. Banchoff - Critical points and curvature for embedded polyhedra, J. Diff. Geom. 1 (1967), 245-256. | MR 225327 | Zbl 0164.22903

[BB] L. Bérard Bergery - La courbure scalaire des variétés riemanniennes, Sém. Bourbaki 1979/80, exposé n° 556, Springer-Verlag, Lect. Notes in Math. 842(1981), 225-245. | Numdam | MR 636526 | Zbl 0461.53023

[Br 1] M. Berger - Géométrie, tomes 2 et 3, Cedic-Nathan, Paris, 1980.

[Br 2] M. Berger - La géométrie métrique des variétés riemanniennes, Colloque Elie Cartan, Astérisque, hors série (1985), 9-66. | MR 837193 | Zbl 0615.53028

[B-G] M. Berger et B. Gostiaux - Géométrie différentielle, Armand Colin, Paris, 1972. | MR 494180 | Zbl 0251.53001

[B-K] P. Buser et H. Karcher - Gromov's almost flat manifolds, Astérisque 81, (Société Mathématique de France). | MR 619537 | Zbl 0459.53031

[C 1] J. Cheeger - On the Hodge theory of Riemannian pseudomanifolds, Proc. Symp. Pure Math. A.M.S. 36 (1980), 91-145. | MR 573430 | Zbl 0461.58002

[C 2] J. Cheeger - Spectral Geometry of Singular Riemannian Spaces, J. Diff. Geom. 18 (1983), 575-657. | MR 730920 | Zbl 0529.58034

[C 3] J. Cheeger - A Vanishing Theorem for Piecewise Constant Curvature Spaces, pré-publication Stony Brook.

[C-M-S 1] J. Cheeger, W. Müller, R. Schrader - Lattice Gravity or Riemannian Structure on Piecewise Linear Spaces, in Unified théories of elementary particles (Heisenberg Symposium 1981), Lect. Notes in Phys., Breitenlohner P., dürr, H.P. (eds), Springer, 1982. | MR 822799

[C-M-S 2] J. Cheeger, W. Müller, R. Schrader - On the Curvature of Piecewise Flat Spaces, Commun. Math. Phys. 92 (1984), 405-454. | MR 734226 | Zbl 0559.53028

[C-M-S 3] J. Cheeger, W. Müller, R. Schrader - Kinematic and tube formulas for Piecewise Linear Spaces, pré-publication Stony Brook.

[Ch 1] S. S. Chern - A simple intrinsic proof of the Gauss - Bonnet formula for closed Riemannian manifolds, Ann. Math. 45 (1944) , 747-752. | MR 11027 | Zbl 0060.38103

[Ch 2] S. S. Chern - On the kinematic formula in integral geometry, J. Math. Mech. 16 (1966), 101-118. | MR 198406 | Zbl 0142.20704

[CV] Y. Colin De Verdière - Propriétés asymptotiques de l'équation de la chaleur sur une variété compacte, d'après P. Gilkey, Sém. Bourbaki 1973/ 74, exposé n° 439, Springer-Verlag, Lect. Notes in Math. 431(1975), 58-68. | Numdam | MR 426069 | Zbl 0324.58019

[D] H. Donnelly - Heat equation and the volume of tubes, Inv. Math. 29 (1975) , 239-243. | MR 402832 | Zbl 0293.35035

[F] H. Federer - Curvature measures, Trans. Amer. Math. Soc., 93 (1959) , 418- 491. | MR 110078 | Zbl 0089.38402

[Fe] B. V. Fedosov - Asymptotic formulas for the eigenvalues of the Laplace operator for a polyhedron, Dodkl. Akad. Nauk, SSSR, 157 (1964), 536- 538. | MR 164129 | Zbl 0133.36101

[G-M] S. Gallot, D. Meyer - Opérateur de courbure et Laplacien des formes différentielles, J. Math. Pures et Appl., 54 (1975), 285-304. | MR 454884

[Gi] P. Gilkey - Invariance Theory, the Heat Equation, and the Atiyah - Singer Index Theorem, Publish or Perish, Wilmington, 1984. | MR 783634 | Zbl 0565.58035

[Gr] M. Gromov - Structures métriques pour les variétés riemanniennes, rédigé par J. Lafontaine et P. Pansu, Cedic-Nathan, Paris, 1980. | MR 682063 | Zbl 0509.53034

[Ha] H. Hadwiger - Vorlesungen über Inhalt, Oberfläche and Isoperimetrie, Springer-Verlag, Berlin, 1957. | MR 102775 | Zbl 0078.35703

[H] D. Hilbert - Die Grundlagen der Physik, Nach. Ges. Wiss. Göttingen (1915), 461-472.

[K] H. Kneser - Der Simplexinhalt in der nichteuklischen Geometrie, Deutsch. Math. 1 (1936), 337-340. | JFM 62.0653.03

[La] R. Langevin - Courbures, feuilletages et surfaces (mesures et distributions de Gauss), thèse, Orsay, 1980. | MR 584793 | Zbl 0466.53036

[MP] R. Macpherson - The combinatorial formula of Gabrielov, Gelfand and Losik for the first Pontrjagin class, Sém. Bourbaki 1976/77, exposé n° 497, Springer-Verlag, Lect. Notes in Math. 677(1978), 105-124. | Numdam | MR 521763 | Zbl 0388.57013

[M-S-T] C. W. Misner, K. S. Thorn, J. A. Wheeler - Gravitation, Freeman, San Francisco, 1973. | MR 418833

[Mu] W. Müller - Spectral theory for Riemannian manifolds with cusps and a related trace formula, preprint, I.H.E.S., 1982. | MR 674295

[Pa] P. Pansu - Effondrement des variétés riemanniennes, d'après J. Cheeger et M. Gromov, Sém. Bourbaki 1983/84, exposé n° 618, Astérisque 121-122 (1985), 63-82. | Numdam | MR 768954 | Zbl 0551.53020

[P] V. K. Patodi - Curvature and the Eigenforms of the Laplace Operator, J. Diff. Geom. 5(1971), 233-249. | MR 292114 | Zbl 0211.53901

[R] T. Regge - General Relativity without coordinates, Nuovo Cimento 19 (1961), 551-571. | MR 127372

[Ra] T. Rado - Length and area, Amer. Math. Soc. Coll. Publications, 30(1948). | Zbl 0033.17002

[S] L. A. Santalo - Integral Geometry and Geometric Probability, Addison-Wesley, Reading, 1976. | MR 433364 | Zbl 0342.53049

[Sc] L. Schläfli - Gesammelte Werke, Birkhaüser.

[Sp] M. Spivak - Differential Geometry, t. 5, Publish or Perish.

[St] D. Stone - Geodesics in piecewise linear manifolds, Trans. Amer. Math. Soc., 215 (1976), 1-44. | MR 402648 | Zbl 0328.53033

[S-W] R. Sulanke, P. Wintgen - Differential Geometrie and Faserbündel, Birkhaüser, Berlin, 1972. | MR 413153 | Zbl 0271.53035

[W] H. Weyl - On the volume of tubes, Amer. J. of Math. 61 (1939), 461-472. | JFM 65.0796.01 | MR 1507388

[Wh] H. Whitney - Geometric Integration Theory, Princeton University Press, Princeton, 1957. | MR 87148 | Zbl 0083.28204

[Wi] P. Wintgen - Normal cycle and integral curvature for polyhedra in Riemannian manifolds, Colloquia Mathematica Societatis Janos Bolya, Budapest, 1978. | Zbl 0509.53037