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On successive minima and intrinsic volumes
Author(s) -
Schnell U.,
Wills J. M.
Publication year - 1993
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300013772
Subject(s) - mathematics , maxima and minima , regular polygon , euclidean space , integer lattice , euclidean geometry , convex body , combinatorics , integer (computer science) , lattice (music) , pure mathematics , inequality , mathematical analysis , geometry , convex hull , condensed matter physics , half integer , physics , computer science , acoustics , programming language
In Euclidean d ‐space E d we prove inequalities between the intrinsic volumes ( i.e. , normalized quermassintegrals) of convex bodies and the successive minima of arbitrary lattices. The inequalities are tight and they generalize earlier results of Hadwiger and Henk for the integer lattice ℤ d .