Peano curves with smooth footprints

Jairo Bochi, Pedro H. Milet

Research output: Contribution to journalArticlepeer-review


We construct Peano curves γ: [0, ∞) → R2 whose “footprints” γ([0, t]) , t > 0, have C boundaries and are tangent to a common continuous line field on the punctured plane R2\ {γ(0)}. Moreover, these boundaries can be taken C-close to any prescribed smooth family of nested smooth Jordan curves contracting to a point.

Original languageEnglish (US)
Pages (from-to)693-712
Number of pages20
JournalMonatshefte fur Mathematik
Issue number4
StatePublished - Aug 1 2016

All Science Journal Classification (ASJC) codes

  • General Mathematics


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