2014/07/19 by Bochi, Jairo, Milet, Pedro H.
#26A30 #26E10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1407.5204
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.