Peano Curves with Smooth Footprints
نویسنده
چکیده
We construct Peano curves γ : r0,8q Ñ R2 whose “footprints” γpr0, tsq, t ą 0, have C8 boundaries and are tangent to a common continuous line field on the punctured plane R2 r tγp0qu. Moreover, these boundaries can be taken C8-close to any prescribed smooth family of nested smooth Jordan curves contracting to a point.
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