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Paper detail

Hyperplane families creating envelopes

A simple geometric mechanism: "the locus of intersections of perpendicular bisectors and normal lines", often arises in many guises in Nonlinear Sciences. In this paper, a new application of this simple geometric mechanism is given. Namely, we show that this mechanism gives answers to all four basic problems on envelopes created by hyperplane families (existence problem, representation problem, equivalence problem of definitions, uniqueness problem) at once.

preprint2022arXivOpen access
Takashi Nishimura
math.GTmath.DG
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Takashi Nishimura

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