Polar DuaLs of Convex Bodies

Abstract

A generalization and the dual version of the following result due to Firey is given: The mixed area of a plane convex body and its polar dual is at least Pi. We give a sharp upper bound for the product of the dual cross-sectional measure of any index and that of its polar dual. A general result for a convex body Kappa and a convex increasing real valued function gives inequalities for sets of constant width and sets with equichordal points as special cases. Keywords: Polar duals; Convex bodies.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1990
Accession Number
ADA218081

Entities

People

  • Mostafa Ghandehari

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Arithmetic
  • Availability
  • Bodies
  • Convex Bodies
  • Convex Sets
  • Differential Equations
  • Equations
  • Geometry
  • Inequalities
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Numbers
  • Polynomials
  • Real Numbers
  • Security
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Gender and Food Studies
  • Graph Algorithms and Convex Optimization.