Curvature measures
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- by Herbert Federer
- Trans. Amer. Math. Soc. 93 (1959), 418-491
- DOI: https://doi.org/10.1090/S0002-9947-1959-0110078-1
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References
- Carl B. Allendoerfer, The Euler number of a Riemann manifold, Amer. J. Math. 62 (1940), 243–248. MR 2251, DOI 10.2307/2371450
- Carl B. Allendoerfer and André Weil, The Gauss-Bonnet theorem for Riemannian polyhedra, Trans. Amer. Math. Soc. 53 (1943), 101–129. MR 7627, DOI 10.1090/S0002-9947-1943-0007627-9 Blaschke BL. Vorlesungen über Integralgeometrie, Leipzig and Berlin, Teubner, 1936-1937. Bonnesen and W. Fenchel BF. Theorie der konvexen Körper, Erg. d. Math. vol. 3 (1934) pp. 1-172.
- N. Bourbaki, Éléments de mathématique. VII. Première partie: Les structures fondamentales de l’analyse. Livre II: Algèbre. Chapitre III: Algèbre multilinéaire, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1044, Hermann & Cie, Paris, 1948 (French). MR 0026989 Intégration, Actualités Sci. Ind. no. 1175, 1952. É. Cartan CA. Leçons sur la géométrie des espaces de Riemann, Paris, Gauthier-Villars, 1946.
- Lamberto Cesari, Surface area, Annals of Mathematics Studies, No. 35, Princeton University Press, Princeton, N. J., 1956. MR 0074500
- Shiing-shen Chern, On the curvatura integra in a Riemannian manifold, Ann. of Math. (2) 46 (1945), 674–684. MR 14760, DOI 10.2307/1969203
- Shiing-shen Chern, On the kinematic formula in the Euclidean space of $n$ dimensions, Amer. J. Math. 74 (1952), 227–236. MR 47353, DOI 10.2307/2372080 La géométrie des sousvariétés d’un espace euclidien à plusieurs dimensions, L’Ens. Math. vol. 40 (1955) pp. 26-46.
- Shiing-shen Chern and Richard K. Lashof, On the total curvature of immersed manifolds, Amer. J. Math. 79 (1957), 306–318. MR 84811, DOI 10.2307/2372684
- Maurice R. Demers and Herbert Federer, On Lebesgue area. II, Trans. Amer. Math. Soc. 90 (1959), 499–522. MR 102586, DOI 10.1090/S0002-9947-1959-0102586-4
- Ennio De Giorgi, Su una teoria generale della misura $(r-1)$-dimensionale in uno spazio ad $r$ dimensioni, Ann. Mat. Pura Appl. (4) 36 (1954), 191–213 (Italian). MR 62214, DOI 10.1007/BF02412838
- Herbert Federer, Surface area. I, Trans. Amer. Math. Soc. 55 (1944), 420–437. MR 10610, DOI 10.1090/S0002-9947-1944-0010610-1
- Herbert Federer, Surface area. II, Trans. Amer. Math. Soc. 55 (1944), 438–456. MR 10611, DOI 10.1090/S0002-9947-1944-0010611-3
- Herbert Federer, Coincidence functions and their integrals, Trans. Amer. Math. Soc. 59 (1946), 441–466. MR 15466, DOI 10.1090/S0002-9947-1946-0015466-0
- Herbert Federer, The $(\varphi ,k)$ rectifiable subsets of $n$-space, Trans. Amer. Math. Soc. 62 (1947), 114–192. MR 22594, DOI 10.1090/S0002-9947-1947-0022594-3
- Herbert Federer, Dimension and measure, Trans. Amer. Math. Soc. 62 (1947), 536–547. MR 23325, DOI 10.1090/S0002-9947-1947-0023325-3
- Herbert Federer, Measure and area, Bull. Amer. Math. Soc. 58 (1952), 306–378. MR 49289, DOI 10.1090/S0002-9904-1952-09586-0
- Herbert Federer, Some integralgeometric theorems, Trans. Amer. Math. Soc. 77 (1954), 238–261. MR 63686, DOI 10.1090/S0002-9947-1954-0063686-6
- Herbert Federer, On Lebesgue area, Ann. of Math. (2) 61 (1955), 289–353. MR 67178, DOI 10.2307/1969917 An introduction to differential geometry, Mimeographed lecture notes, Brown University, 1948.
- W. Fenchel, On total curvatures of Riemannian manifolds: I, J. London Math. Soc. 15 (1940), 15–22. MR 2252, DOI 10.1112/jlms/s1-15.1.15
- Werner Fenchel, On the differential geometry of closed space curves, Bull. Amer. Math. Soc. 57 (1951), 44–54. MR 40040, DOI 10.1090/S0002-9904-1951-09440-9
- Harley Flanders, Development of an extended exterior differential calculus, Trans. Amer. Math. Soc. 75 (1953), 311–326. MR 57005, DOI 10.1090/S0002-9947-1953-0057005-8
- Harley Flanders, Methods in affine connection theory, Pacific J. Math. 5 (1955), 391–431. MR 75651
- H. Hadwiger, Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). MR 0102775
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
- Lynn H. Loomis, The intrinsic measure theory of Riemannian and Euclidean metric spaces, Ann. of Math. (2) 45 (1944), 367–374. MR 9976, DOI 10.2307/1969274
- Lynn H. Loomis, Abstract congruence and the uniqueness of Haar measure, Ann. of Math. (2) 46 (1945), 348–355. MR 11713, DOI 10.2307/1969028
- Marston Morse, The calculus of variations in the large, American Mathematical Society Colloquium Publications, vol. 18, American Mathematical Society, Providence, RI, 1996. Reprint of the 1932 original. MR 1451874, DOI 10.1090/coll/018
- J. W. Milnor, On the total curvature of knots, Ann. of Math. (2) 52 (1950), 248–257. MR 37509, DOI 10.2307/1969467 Radó R. Length and area, Amer. Math. Soc. Colloquium Publications, vol. 30, 1948, 572 pp. Saks S. Theory of the integral, Monografie Matematyczne, vol. 7, Warsaw, 1937. A. Santaló SA. Über das kinematische Mass im Raum, Actualités Sci. Ind. no. 357, 1936.
- Hermann Weyl, On the Volume of Tubes, Amer. J. Math. 61 (1939), no. 2, 461–472. MR 1507388, DOI 10.2307/2371513
- Hassler Whitney, On totally differentiable and smooth functions, Pacific J. Math. 1 (1951), 143–159. MR 43878
- Hassler Whitney, Geometric integration theory, Princeton University Press, Princeton, N. J., 1957. MR 0087148
Bibliographic Information
- © Copyright 1959 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 93 (1959), 418-491
- MSC: Primary 53.00
- DOI: https://doi.org/10.1090/S0002-9947-1959-0110078-1
- MathSciNet review: 0110078