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On Heilbronn’s Problem in Higher Dimension

✍ Scribed by Hanno Lefmann


Publisher
Springer-Verlag
Year
2003
Tongue
English
Weight
190 KB
Volume
23
Category
Article
ISSN
0209-9683

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Given a lattice L=AZ 3 with determinant d(L)= |det(A)| >0, let }(L)= sup[vol(P)Â(8d(L)] where the supremum is taken over all o-symmetric parallelepipeds P with faces parallel to the coordinate axes such that P & L= [o]. We prove the following conjecture by Gruber: The absolute minimum of the functio