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Krickeberg, Klaus

Über den Gaußschen und den Stokesschen Integralsatz. III. (German) Zbl 0057.13304

Math. Nachr. 12, 341-365 (1954).
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Differential geometry
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\textit{K. Krickeberg}, Math. Nachr. 12, 341--365 (1954; Zbl 0057.13304)
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[1] Lagrange, Nouvelles recherches sur la nature et la propagation du son. Miscellanea Taurinensia 2 pp 45– (1760)
[2] Oeuvres 1 pp 263– (1867)
[3] Gauss, Theoria attractionis corporum sphaeroidicorum ellipticorum homogeneorum methodo nova tractata. Commentationes societatis regiae scientiarum Gottingensis recentiores 2 pp 2– (1813)
[4] Werke 5 pp 5– (1877)
[5] 1828 An essay on the application of mathematical analysis to the theories of electricity and magnetism. Nottingham, Art. 3;
[6] J. reine angew. Math. 44 pp 360– (1852)
[7] Ostrogradsky, Mém. Acad. Impér. Sci. de St. Pétersbourg, Sci. math. phys. natur., VI. Sér. 1 pp 129– (1831)
[8] Ostrogradsky, Mém. Acad. Impér. Sci. de St. Pétersbourg, Sci. math. phys. natur., VI. Sér. 3 pp 35– (1838)
[9] 1851 Grundlagen für eine allgemeine Theorie der Funktionen einer veränderlichen komplexen Größe. Göttingen, S. 8–9;
[10] Werke Leipzig 1876, S. 12–14.
[11] 1854 Smith’s prize examination paper. Cambridge Univ. Calendar;
[12] Math. and Phys. Papers 5 pp 320– (1905)
[13] 1861 Schwere, Elektrizität und Magnetismus. Vorlesung Univ. Göttingen, herausgegeben von K. Hattendorf, Hannover 1876, S. 252–254.
[14] 1861 Zur allgemeinen Theorie der Bewegung der Flüssigkeiten. Göttingen, S. 34–37.
[15] Ostrogradsky, Sur une intégrale définie. Bull. Acad. Impér. Sci. de St. Pétersbourg 3 pp 65– (1861)
[16] Betti, Ann. Mat. pura appl., II. Ser. 4 pp 140– (1870)
[17] 1873 Treatise on Electricity and Magnetism. I. Oxford, Art. 24, S. 25–27.
[18] Poincaré, Sur les résidus des intégrales doubles. Acta math. 9 pp 321– (1887)
[19] Oeuvres 3 pp 446– (1934) · JFM 46.0034.12
[20] 1894 Leçons sur la théorie générale des surfaces. III. Paris, S. 122–125.
[21] Poincaré, J. École polytechn., II. Sér. 1 pp 1– (1895)
[22] Franchis, Rend. Circ. mat. Palermo 12 pp 163– (1898)
[23] 1899 Les méthodes nouvelles de la mécanique céleste. III. Paris, S. 10.
[24] Pringsheim, S. - Ber. math.-naturw. Kl. Bayer. Akad. Wiss. München 29 pp 39– (1899)
[25] Hamburger, J. reine angew. Math. 124 pp 28– (1902)
[26] Porter, Ann. of Math., II. Ser. 7 pp 1– (1905)
[27] Poli, Atti Accad. Sci. Torino, Cl. Sci. fis. mat. natur. 49 pp 218– (1914)
[28] Amer. J. Math. 36 pp 137– (1914)
[29] Gross, Das isoperimetrische Problem bei Doppelintegralen. Monatsh. Math. Phys. 27 pp 70– (1916)
[30] Lichtenstein, Arch. Math Phys., III. Ser. 27 pp 31– (1918)
[31] Daniell, Integrals around general boundaries. Bull. Amer. math. soc. 25 pp 65– (1918) · JFM 47.0240.03 · doi:10.1090/S0002-9904-1918-03148-0
[32] Brouwer, Opmerking over meervoudige integralen. Amst. Ak. Versl. 28 pp 116– (1919) · JFM 47.0906.03
[33] Picone, Atti Accad. naz. Lincei, Rend., Cl. Sci. fis. mat. natur., V. Ser. 28 pp 270– (1919)
[34] Picone, Sul teorema di Green nel piano e nello spazio. Rend. Circ. mat. Palermo 43 pp 239– (1919) · JFM 47.0453.03 · doi:10.1007/BF03014672
[35] van Vleck, Ann. of Math., II. Ser. 22 pp 226– (1921)
[36] 1922 Traité d’Analyse. I. 3. Aufl., Paris, S. 142–145.
[37] Franklin, Ann of Math., II. Ser. 24 pp 213– (1923)
[38] Pollard, Proc. London math. Soc., II. Ser. 21 pp 456– (1923)
[39] 1923 Invariantentheorie. Groningen, S. 338–340.
[40] 1924 Der Ricci-Kalkül. Berlin, S. 95–98.
[41] Bray, Ann. of Math., II. Ser. 26 pp 278– (1925)
[42] Young, Proc. London math. Soc., II. Ser. 24 pp 21– (1925)
[43] Buhl, Formules stokiennes. Mém. Sci. math. 16 (1926)
[44] Schauder, The theory of surface measure. Fundamenta Math. 8 pp 1– (1926)
[45] Mullings, The rotational derivative and some applications. Amer. math. Monthly 34 pp 241– (1927) · JFM 53.0716.05
[46] Szücs, Acta Sci. math., Szeged 3 pp 81– (1927)
[47] 1928 Bemerkungen über den Stokesschen Satz. Bull. intern. Acad. Pol. Sci. Lett., Cl. Sci. math. nat., Sér. A, 1–6.
[48] Smith, Trans. Amer. math. Soc. 30 pp 405– (1928)
[49] 1929 Foundations of Potential Theory. Berlin, S. 84–121.
[50] Caccioppoli, Rend. Circ. mat. Palermo 54 pp 217– (1930)
[51] 1930 Lehrbuch der Differentialgeometrie. II. Leipzig, S. 237–240.
[52] 1931 Vorlesungen über Differential- und Integralrechnung. II. 2. Aufl., Berlin, S. 318–321.
[53] 1933 Knopp, Einführung in die höhere Mathematik. III. 6. Aufl., Leipzig, S. 428–431 u. 449–452.
[54] Estermann, Math. Z. 37 pp 556– (1933)
[55] 1933 Cours d’analyse mathématique. I. 5. Aufl., Paris, S. 338–340.
[56] Favard, Ann. sci. École norm. sup., III. Sér. 51 pp 1– (1934)
[57] Morrey, A class of representations of manifolds. I. II. Amer. J. Math. 55 pp 683– (1933) · Zbl 0008.07202
[58] A class of representations of manifolds. I. II. Amer. J. Math. 56 pp 275– (1934)
[59] Lebesgue, Sur la mesure des grandeurs. Enseignement math. 33 pp 176– (1935) · JFM 61.0965.03
[60] Randolph, Carathéodory measure and and a generalization of the Gauß-Green Lemma. Trans. Amer. math. Soc. 38 pp 531– (1935) · JFM 61.0241.02
[61] Cairns, The generalized theorem of Stokes. Trans. Amer. math. Soc. 40 pp 167– (1936) · Zbl 0015.12701
[62] Bochner, Remark on the theorem of Green. Duke math. J. 3 pp 334– (1937) · JFM 63.0712.05
[63] Wilkosz, Prace mat.-fiz. 44 pp 109– (1937)
[64] 1938 Aumann, Differential- und Integralrechnung. III. 1. Aufl., Berlin, S. 169–178.
[65] de Possel, Bull. Sci. math., II. Sér. 62 pp 262– (1938)
[66] Maak, Oberflächenintegral und Stokes-Formel im gewöhnlichen Raume. Math. Ann. 116 pp 574– (1939) · Zbl 0020.26102
[67] Schmidt, Math. Z. 44 pp 689– (1939)
[68] Reid, Amer. J. Math. 63 pp 563– (1941)
[69] Ridder, Nieuw Arch. Wiskunde, II. R. 21 pp 28– (1941)
[70] Gillis, Acad. roy. Belgique, Cl. Sci., Mém., Coll 4. II. Sér. 20 (1943)
[71] Federer, The Gauß-Green Theorem. Trans. Amer. math. Soc. 58 pp 44– (1945) · Zbl 0060.14102
[72] 1947 Algèbre et analyse linéaires. Paris, S. 195–196.
[73] Lorentz, Beweis des Gaußschen Integralsatzes. Math. Z. 51 pp 61– (1949)
[74] Verblunsky, J. London math. Soc. 24 pp 146– (1949)
[75] 1949 , Pfaff’s probles and its generalizations. Oxford, S. 67–70.
[76] Iseki, J. math. Soc. Japan 2 pp 114– (1950)
[77] Okamura, Mem. Coll. Sci. Univ. Kyoto, Ser. A 26 pp 5– (1950)
[78] Mizohata, Mem. Coll. Sci. Univ. Kyoto, Ser. A 26 pp 15– (1950)
[79] Mizohata, Mem. Coll. Sci. Univ. Kyoto, Ser. A 26 pp 175– (1950)
[80] Cecconi, Sul teorema di Gauss-Green. Rend. Sem. mat. Univ. Padova 20 pp 194– (1951)
[81] Potts, J. London math. Soc. 26 pp 302– (1951)
[82] Caccioppoli, I, II. Atti Accad. naz. Lincei, Rend., Cl. Sci. fis. mat. natur., VIII. Ser. 12 pp 3– (1952)
[83] Caccioppoli, I, II, III. Atti Accad. naz. Lincei, Rend., Cl. Sci. fis. mat. natur., VIII. Ser. 12 pp 219– (1952)
[84] Cecconi, Sul teorema di Stokes. Rivista. Mat. Univ. Parma 3 pp 233– (1952)
[85] Stoll, Teil: Mehrfache Integrale auf komplexen Mannigfaltigkeiten. Math. Z. 57 pp 116– (1952) · Zbl 0047.32401
[86] Caccioppoli, Atti IV. Congr. Un. mat. Ital. 2 pp 41– (1953)
[87] 1953 Der Begriff der Ergiebigkeit eines Vektorfeldes und der Gaußsche Integralsatz. Ber. Math. Tagung Berlin 1953. · Zbl 0052.38203
[88] 1954 , Differential- und Integralrechnung. III. 2. Aufl., Berlin, Nr. 11.
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