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Caustics of convex curves

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1-W8-34, O-okayama Meguro-ku, Tokyo 152-8552, Japan

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and

Masaaki Umehara

Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1-W8-34, O-okayama Meguro-ku, Tokyo 152-8552, Japan

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https://doi.org/10.1142/S0218216514500503Cited by:4 (Source: Crossref)

Abstract

It is well-known that the focal set (i.e. the image of the caustic) of a given convex closed curve γ admits singular points. In this paper, we classify the diffeomorphic type of focal sets of convex curves which admit at most four cusps.

Keywords:

AMSC: Primary: 53A04, Secondary: 58K15, Secondary: 57R17

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