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Schoenberg, I. J.

An isoperimetric inequality for closed curves convex in even-dimensional Euclidean spaces. (English) Zbl 0056.15705

Acta Math. 91, 143-164 (1954).
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Cited in 1 Review
Cited in 22 Documents

Keywords:

Metric geometry, convex geometry, integral geometry
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References:

[1] T. Bonnesen andW. Fenchel, Theorie der konvexen Körper,Ergebnisse der Mathematik, 3, Heft 1 (1934).
[2] C. Carathéodory, Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen,Rendiconti di Palermo, 32 (1911), 193–217. · JFM 42.0429.01 · doi:10.1007/BF03014795
[3] C. Carathéodory,Variationsrechnung und partielle Differentialgleichungen erster Ordnung, Leipzig, 1935. · Zbl 0011.35603
[4] F. Gantmakher andM. Krein,Oscillatory matrices and kernels and small vibrations of mechanical systems (in Russian), 2nd Ed., Moscow, 1950.
[5] W. Gustin, Sets of finite planar order,Duke Math. Journal, 14 (1947), 51–66. · Zbl 0030.07503 · doi:10.1215/S0012-7094-47-01406-3
[6] J. Hadamard, Résolution d’une question relative aux déterminants,Bulletin des sciences mathématiques, (2), 17 (1893), 240–248. · JFM 25.0221.02
[7] J. Hjelmslev, Introduction à la théorie des suites monotones,Oversigt over det Kgl. Danske Videnskabernes Selskabs Forhandlinger, 1914, 1–74.
[8] A. Hurwitz, Sur le problème des isopérimétres,Comptes Rendus, 132 (1901), 401–403; also inMath. Werke 1, 490–491. · JFM 32.0386.01
[9] A. Marchaud, Sur les continus d’ordre borné,Acta Mathematica 55 (1930), 67–115. · JFM 56.0512.05 · doi:10.1007/BF02546510
[10] J. von Neumann andI. J. Schoenberg, Fourier integrals and metric geometry,Transactions of the Amer. Math. Society, 50 (1941), 226–251. · Zbl 0028.41002
[11] G. Pólya andG. Szegö,Aufgaben und Lehrsätze aus der Analysis, II, Berlin, 1925.
[12] G. Pólya On the mean-value theorem corresponding to a given linear homogeneous differential equation,Transactions of the Amer. Math. Society, 24 (1922), 312–324.
[13] Peter Scherk, Über differenzierbare Kurven und Bögen,Časopis pro pěstováni Matematiky a Fysiky 66 (1937), 165–191. · Zbl 0016.22703
[14] I. J. Schoenberg andAnne Whitney, A theorem on polygons inn dimensions with applications to variation-diminishing and cyclic variation-diminishing linear transformations,Compositio Mathematica, 9 (1951), 141–160. · Zbl 0043.25204
[15] I. J. Schoenberg, On smoothing operations and their generating functions,Bulletin of the Amer. Math. Society, 59 (1953), 199–230. · Zbl 0050.28703 · doi:10.1090/S0002-9904-1953-09695-1
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