We give asymptotic estimates for the number of non-overlapping homothetic
copies of some centrally symmetric oval B which have a common point with a
2-dimensional domain F having rectifiable boundary, extending previous work
of the L.Fejes-Toth, K.Borockzy Jr., D.G.Larman, S.Sezgin, C.Zong and the
authors. The asymptotics compute the length of the boundary βF in the
Minkowski metric determined by B. The core of the proof consists of a method
for sliding convex beads along curves with positive reach in the Minkowski
plane. We also prove that level sets are rectifiable subsets, extending a
theorem of Erd\"os, Oleksiv and Pesin for the Euclidean space to the Minkowski
space.Comment: 20p, 9 figure