On finite lattice coverings |
| |
Authors: | Martin Meyer Uwe Schnell |
| |
Institution: | Mathematisches Institut, Universit?t Siegen, 57068 Siegen, Germany, e-mail: meyer@mathematik.uni-siegen.de; schnell@mathematik.uni-siegen.de, DE
|
| |
Abstract: | We consider finite lattice coverings of strictly convex bodies K. For planar centrally symmetric K we characterize the finite arrangements C
n
such that conv , where C
n
is a subset of a covering lattice for K (which satisfies some natural conditions). We prove that for a fixed lattice the optimal arrangement (measured with the parametric
density) is either a sausage, a so-called double sausage or tends to a Wulff-shape, depending on the parameter. This shows
that the Wulff-shape plays an important role for packings as well as for coverings. Further we give a version of this result
for variable lattices. For the Euclidean d-ball we characterize the lattices, for which the optimal arrangement is a sausage, for large parameter.
Received 19 May 1999. |
| |
Keywords: | : Covering Lattice Covering Convex Body Wulff-shape |
本文献已被 SpringerLink 等数据库收录! |
|