×

zbMATH — the first resource for mathematics

Curvature measures. (English) Zbl 0089.38402

PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Carl B. Allendoerfer, The Euler number of a Riemann manifold, Amer. J. Math. 62 (1940), 243 – 248. · Zbl 0024.35101
[2] Carl B. Allendoerfer and André Weil, The Gauss-Bonnet theorem for Riemannian polyhedra, Trans. Amer. Math. Soc. 53 (1943), 101 – 129. · Zbl 0060.38102
[3] Blaschke BL. Vorlesungen über Integralgeometrie, Leipzig and Berlin, Teubner, 1936-1937.
[4] Bonnesen and W. Fenchel BF. Theorie der konvexen Körper, Erg. d. Math. vol. 3 (1934) pp. 1-172. · Zbl 0008.07708
[5] N. Bourbaki, Éléments de mathématique. VII. Première partie: Les structures fondamentales de l’analyse. Livre II: Algèbre. Chapitre III: Algèbre multilinéaire, Actualités Sci. Ind., no. 1044, Hermann et Cie., Paris, 1948 (French). · Zbl 0039.25902
[6] Intégration, Actualités Sci. Ind. no. 1175, 1952.
[7] É. Cartan CA. Leçons sur la géométrie des espaces de Riemann, Paris, Gauthier-Villars, 1946.
[8] Lamberto Cesari, Surface area, Annals of Mathematics Studies, no. 35, Princeton University Press, Princeton, N. J., 1956. · Zbl 0683.53003
[9] Shiing-shen Chern, On the curvatura integra in a Riemannian manifold, Ann. of Math. (2) 46 (1945), 674 – 684. · Zbl 0060.38104
[10] Shiing-shen Chern, On the kinematic formula in the Euclidean space of \? dimensions, Amer. J. Math. 74 (1952), 227 – 236. · Zbl 0046.16101
[11] La géométrie des sousvariétés d’un espace euclidien à plusieurs dimensions, L’Ens. Math. vol. 40 (1955) pp. 26-46. · Zbl 0064.17504
[12] Shiing-shen Chern and Richard K. Lashof, On the total curvature of immersed manifolds, Amer. J. Math. 79 (1957), 306 – 318. · Zbl 0078.13901
[13] Maurice R. Demers and Herbert Federer, On Lebesgue area. II, Trans. Amer. Math. Soc. 90 (1959), 499 – 522. · Zbl 0086.04801
[14] Ennio De Giorgi, Su una teoria generale della misura (\?-1)-dimensionale in uno spazio ad \? dimensioni, Ann. Mat. Pura Appl. (4) 36 (1954), 191 – 213 (Italian). · Zbl 0055.28504
[15] Herbert Federer, Surface area. I, Trans. Amer. Math. Soc. 55 (1944), 420 – 437. · Zbl 0060.14003
[16] Herbert Federer, Surface area. II, Trans. Amer. Math. Soc. 55 (1944), 438 – 456. · Zbl 0060.14003
[17] Herbert Federer, Coincidence functions and their integrals, Trans. Amer. Math. Soc. 59 (1946), 441 – 466. · Zbl 0060.14101
[18] Herbert Federer, The (\?,\?) rectifiable subsets of \?-space, Trans. Amer. Soc. 62 (1947), 114 – 192. · Zbl 0032.14902
[19] Herbert Federer, Dimension and measure, Trans. Amer. Math. Soc. 62 (1947), 536 – 547. · Zbl 0032.15001
[20] Herbert Federer, Measure and area, Bull. Amer. Math. Soc. 58 (1952), 306 – 378. · Zbl 0046.28402
[21] Herbert Federer, Some integralgeometric theorems, Trans. Amer. Math. Soc. 77 (1954), 238 – 261. · Zbl 0058.16405
[22] Herbert Federer, On Lebesgue area, Ann. of Math. (2) 61 (1955), 289 – 353. · Zbl 0065.04002
[23] An introduction to differential geometry, Mimeographed lecture notes, Brown University, 1948.
[24] W. Fenchel, On total curvatures of Riemannian manifolds: I, J. London Math. Soc. 15 (1940), 15 – 22. · Zbl 0026.26401
[25] Werner Fenchel, On the differential geometry of closed space curves, Bull. Amer. Math. Soc. 57 (1951), 44 – 54. · Zbl 0042.40006
[26] Harley Flanders, Development of an extended exterior differential calculus, Trans. Amer. Math. Soc. 75 (1953), 311 – 326. · Zbl 0052.17901
[27] Harley Flanders, Methods in affine connection theory, Pacific J. Math. 5 (1955), 391 – 431. · Zbl 0066.16401
[28] H. Hadwiger, Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957 (German). · Zbl 0078.35703
[29] Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. · Zbl 0060.39808
[30] Lynn H. Loomis, The intrinsic measure theory of Riemannian and Euclidean metric spaces, Ann. of Math. (2) 45 (1944), 367 – 374. · Zbl 0060.13406
[31] Lynn H. Loomis, Abstract congruence and the uniqueness of Haar measure, Ann. of Math. (2) 46 (1945), 348 – 355. · Zbl 0060.13407
[32] 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. · Zbl 0011.02802
[33] J. W. Milnor, On the total curvature of knots, Ann. of Math. (2) 52 (1950), 248 – 257. · Zbl 0037.38904
[34] Radó R. Length and area, Amer. Math. Soc. Colloquium Publications, vol. 30, 1948, 572 pp.
[35] Saks S. Theory of the integral, Monografie Matematyczne, vol. 7, Warsaw, 1937.
[36] A. Santaló SA. Über das kinematische Mass im Raum, Actualités Sci. Ind. no. 357, 1936. · JFM 62.0840.02
[37] Hermann Weyl, On the Volume of Tubes, Amer. J. Math. 61 (1939), no. 2, 461 – 472. · Zbl 0021.35503
[38] Hassler Whitney, On totally differentiable and smooth functions, Pacific J. Math. 1 (1951), 143 – 159. · Zbl 0043.05803
[39] Hassler Whitney, Geometric integration theory, Princeton University Press, Princeton, N. J., 1957. · Zbl 0083.28204
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.