| dbo:abstract |
Die Brunn-Minkowski-Ungleichung bzw. der Satz von Brunn und Minkowski, benannt nach den beiden Mathematikern Hermann Brunn und Hermann Minkowski, ist ein klassischer Lehrsatz auf dem mathematischen Teilgebiet der Konvexgeometrie. Die Ungleichung setzt das Lebesgue-Maß der Minkowski-Summe zweier kompakter Teilmengen des n-dimensionalen euklidischen Raums in Relation zum Lebesgue-Maß dieser beiden Teilmengen. Sie hat zahlreiche Anwendungen und zieht insbesondere die isoperimetrische Ungleichung nach sich. (de) In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space. The original version of the Brunn–Minkowski theorem (Hermann Brunn 1887; Hermann Minkowski 1896) applied to convex sets; the generalization to compact nonconvex sets stated here is due to Lazar Lyusternik (1935). (en) En matemáticas, el teorema de Brunn-Minkowski (o desigualdad de Brunn-Minkowski) es una desigualdad que relaciona los volúmenes (o más generalmente medidas de Lebesgue) de subconjuntos compactos del espacio euclidiano. La versión original del teorema de Brunn-Minkowski (Hermann Brunn 1887; Hermann Minkowski 1896) se aplicó a conjuntos convexos; la generalización a conjuntos compactos no convexos que se indica aquí se debe a (1935). (es) In matematica, il teorema di Brunn-Minkowski (o disuguaglianza di Brunn-Minkowski) è una disuguaglianza che mette in relazione volumi (o, più in generale, misure di Lebesgue) di sottoinsiemi compatti di uno spazio euclideo. La versione originale del teorema di Brunn-Minkowski ( 1887; Hermann Minkowski 1896) si applicava a insiemi convessi; la generalizzazione a insiemi compatti non convessi a cui ci riferiamo qui è dovuta a (1935). (it) Inom matematiken är Brunn–Minkowski sats (eller Brunn–Minkowskis olikhet) en olikhet mellan volymerna (eller mer allmänt Lebesguemåtten) av kompakta delrum av ett Euklidiskt rum. Den ursprungliga formen av satsen ( 1887; Hermann Minkowski 1896) gällde konvexa mängder; generaliseringen till kompakta icke-konvexa mängder bevisades av (1935). (sv) Теорема Брунна — Минковского — классическая теорема выпуклой геометрии: (ru) |
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http://sbubeck.com/Bubeck15.pdf http://www.math.lsa.umich.edu/~barvinok/total710.pdf https://projecteuclid.org/euclid.rae/1212412875 https://archive.org/details/theoryofconvexbo0000bonn https://www.ams.org/journals/bull/2002-39-03/S0273-0979-02-00941-2/ https://www.youtube.com/watch%3Fv=5YI6wKw2Jdo https://www.youtube.com/watch%3Fv=UHvT1MxFuvo https://cs.uwaterloo.ca/~lapchi/cs798/L19.pdf https://cs.uwaterloo.ca/~lapchi/cs798/L20.pdf |
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Die Brunn-Minkowski-Ungleichung bzw. der Satz von Brunn und Minkowski, benannt nach den beiden Mathematikern Hermann Brunn und Hermann Minkowski, ist ein klassischer Lehrsatz auf dem mathematischen Teilgebiet der Konvexgeometrie. Die Ungleichung setzt das Lebesgue-Maß der Minkowski-Summe zweier kompakter Teilmengen des n-dimensionalen euklidischen Raums in Relation zum Lebesgue-Maß dieser beiden Teilmengen. Sie hat zahlreiche Anwendungen und zieht insbesondere die isoperimetrische Ungleichung nach sich. (de) In mathematics, the Brunn–Minkowski theorem (or Brunn–Minkowski inequality) is an inequality relating the volumes (or more generally Lebesgue measures) of compact subsets of Euclidean space. The original version of the Brunn–Minkowski theorem (Hermann Brunn 1887; Hermann Minkowski 1896) applied to convex sets; the generalization to compact nonconvex sets stated here is due to Lazar Lyusternik (1935). (en) En matemáticas, el teorema de Brunn-Minkowski (o desigualdad de Brunn-Minkowski) es una desigualdad que relaciona los volúmenes (o más generalmente medidas de Lebesgue) de subconjuntos compactos del espacio euclidiano. La versión original del teorema de Brunn-Minkowski (Hermann Brunn 1887; Hermann Minkowski 1896) se aplicó a conjuntos convexos; la generalización a conjuntos compactos no convexos que se indica aquí se debe a (1935). (es) In matematica, il teorema di Brunn-Minkowski (o disuguaglianza di Brunn-Minkowski) è una disuguaglianza che mette in relazione volumi (o, più in generale, misure di Lebesgue) di sottoinsiemi compatti di uno spazio euclideo. La versione originale del teorema di Brunn-Minkowski ( 1887; Hermann Minkowski 1896) si applicava a insiemi convessi; la generalizzazione a insiemi compatti non convessi a cui ci riferiamo qui è dovuta a (1935). (it) Inom matematiken är Brunn–Minkowski sats (eller Brunn–Minkowskis olikhet) en olikhet mellan volymerna (eller mer allmänt Lebesguemåtten) av kompakta delrum av ett Euklidiskt rum. Den ursprungliga formen av satsen ( 1887; Hermann Minkowski 1896) gällde konvexa mängder; generaliseringen till kompakta icke-konvexa mängder bevisades av (1935). (sv) Теорема Брунна — Минковского — классическая теорема выпуклой геометрии: (ru) |
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Brunn-Minkowski-Ungleichung (de) Teorema de Brunn-Minkowski (es) Brunn–Minkowski theorem (en) Teorema di Brunn-Minkowski (it) Неравенство Брунна — Минковского (ru) Brunn–Minkowskis sats (sv) |
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