The singular evolutoids set and the extended evolutoids front

In this paper we introduce the notion of the singular evolutoid set which is the set of all singular points of all evolutoids of a fixed smooth planar curve with at most cusp singularities. By the Gauss-Bonnet Theorem for Coherent Tangent Bundles over Surfaces with Boundary (Theorem 2.20 in [ 4 ]) a...

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Bibliographic Details
Published in:Aequationes mathematicae 2022-08, Vol.96 (4), p.849-866
Main Author: Zwierzyński, Michał
Format: Article
Language:English
Subjects:
Analysis
Combinatorics
Mathematics
Mathematics and Statistics
Theorems
Citations: Items that this one cites
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Summary:In this paper we introduce the notion of the singular evolutoid set which is the set of all singular points of all evolutoids of a fixed smooth planar curve with at most cusp singularities. By the Gauss-Bonnet Theorem for Coherent Tangent Bundles over Surfaces with Boundary (Theorem 2.20 in [ 4 ]) applied to the extended front of evolutoids of a hedgehog we obtain an integral equality for smooth periodic curves.
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-022-00873-7