MINKOWSKI SYMMETRY SETS OF PLANE CURVES

Author(s)

Reeve, Graham Mark ; Tari, Farid

• Document type: Journal article
• Source: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY; v. 60, n. 2, p. 461-480, MAY 2017.
• Web of Science Citations: 0

Abstract

We study the Minkowski symmetry set of a closed smooth curve. in the Minkowski plane. We answer the following question, which is analogous to one concerning curves in the Euclidean plane that was treated by Giblin and O'Shea (1990): given a point p on gamma, does there exist a bi-tangent pseudo-circle that is tangent to. both at p and at some other point q on gamma? The answer is yes, but as pseudo-circles with non-zero radii have two branches (connected components) it is possible to refine the above question to the following one: given a point p on., does there exist a branch of a pseudo-circle that is tangent to. both at p and at some other point q on.? This question is motivated by the earlier quest of Reeve and Tari (2014) to define the Minkowski Blum medial axis, a counterpart of the Blum medial axis of curves in the Euclidean plane. (AU)

• FAPESP's process: 14/00304-2 - Singularities of differentiable mappings: theory and applications
• Grantee: Maria Aparecida Soares Ruas
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 12/05326-9 - The Minkowski symmetry set and skeletal structures
• Grantee: Graham Mark Reeve
• Support Opportunities: Scholarships in Brazil - Post-Doctoral