78 research outputs found
Asymptotics of generalized Hadwiger numbers ∗
No full textWe give asymptotic estimates for the number of non-overlapping homothetic copies of B which have a common point with F, extending previous work of the L.Fejes-Toth, K.Borockzy Jr., D.G.Larman, S.Sezgin, C.Zong and the authors.
Asymptotics of generalized Hadwiger numbers
No full text20p, 9 figuresWe give asymptotic estimates for the number of non-overlapping homothetic copies of some centrally symmetric oval which have a common point with a 2-dimensional domain 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 in the Minkowski metric determined by . 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 Erdös, Oleksiv and Pesin for the Euclidean space to the Minkowski space
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