TY - JOUR
T1 - Peano curves with smooth footprints
AU - Bochi, Jairo
AU - Milet, Pedro H.
N1 - Publisher Copyright:
© 2016, Springer-Verlag Wien.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00605-016-0899-8
DO - 10.1007/s00605-016-0899-8
M3 - Article
AN - SCOPUS:84961636986
SN - 0026-9255
VL - 180
SP - 693
EP - 712
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
IS - 4
ER -