Konvexe Mengen Book by K. Leichtweiss - Bookswagon
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Konvexe Mengen

Konvexe Mengen


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About the Book

Die Theorie der konvexen Mengen stellt insofern eine besonders reizvolle mathe- matische Disziplin dar, als es in ihrem Rahmen moglich ist, aus wenigen, anschau- lich unmittelbar einsichtigen Voraussetzungen geometrisch wie analytisch in glei- cher Weise wichtige SchluBfolgerungen herzuleiten. Es erscheint daher nicht ver- wunderlich, daB es dem interessierten Laien hierbei schneller als bei anderen mathe- matischen Gebieten gelingen diirfte, sich einzuarbeiten und zu den Gegenstanden aktueller Forschung vorzustoBen. Eine Hilfestellung hierzu zu geben ist das Ziel dieses Buches. Es will kein neuer Ergebnisbericht im Stil des klassischen Werkes von BONNESEN-FENCHEL [3], sondern eine Einfiihrung in die Theorie der konvexen Untermengen eines affinen bzw. euklidischen Raumes sein. Urn diesem Anspruch gerecht zu werden, wurde besonderer Wert darauf gelegt, die behandelten Gegenstande so ausfiihrlich und vollstandig wie moglich darzustellen. Dies hatte bei dem begrenzten Umfang des Buches natiirlich eine zugegebener- maBen subjektive Stoffauswahl zur Folge, in welcher die Inhaltslehre und die Symmetrisierung konvexer Mengen eine bevorzugte Rolle spielen. Die diesbeziig- lichen Uberlegungen gipfeln im Nachweis der Giiltigkeit der verallgemeinerten Ungleichungen von BRUNN-MINKOWSKI nebst Gleichheitsdiskussion. Dagegen wurde auf eine eingehendere Behandlung der Theorie der konvexen Polytope verzichtet; diese findet sich in den Lehrbiichern von B. GRUNBAUM [7] und McMuL- LEN -SHEPHARD [1]. Weiter blie ben funktionalanalytische Verallgemeinerungen auBer Betracht; in diesem Zusammenhang sei der Leser auf das Buch von F. VALEN- TINE [2] verwiesen. Auch auf Fragen iiber konvexe Korper mit Gitterpunkten, die in letzter Zeit durch Arbeiten von H. HADWIGER und J.


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Product Details
  • ISBN-13: 9783540090717
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Height: 244 mm
  • No of Pages: 330
  • Series Title: Hochschultext
  • Weight: 580 gr
  • ISBN-10: 3540090711
  • Publisher Date: 10 Jul 1980
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Spine Width: 18 mm
  • Width: 170 mm


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