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Convex Bodies in Exceptional Relative Positions
Author(s) -
Schneider Rolf
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007978
Subject(s) - intersection (aeronautics) , mathematics , hyperplane , convex body , position (finance) , general position , measure (data warehouse) , convex set , euclidean space , regular polygon , convex hull , boundary (topology) , combinatorics , geometry , point (geometry) , haar , mathematical analysis , computer science , convex optimization , economics , artificial intelligence , wavelet , finance , database , engineering , aerospace engineering
Two convex bodies K and K ′ in Euclidean space E n can be said to be in exceptional relative position if they have a common boundary point at which the linear hulls of their normal cones have a non‐trivial intersection. It is proved that the set of rigid motions g for which K and gK ′ are in exceptional relative position is of Haar measure zero. A similar result holds true if ‘exceptional relative position’ is defined via common supporting hyperplanes. Both results were conjectured by S. Glasauer; they have applications in integral geometry.