Fourier dimension of Mandelbrot cascades on planar curves

Donggeun Ryou; Ville Suomala

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Fourier dimension of Mandelbrot cascades on planar curves

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arxiv 2603.25615 v2 pith:YJBLRAIB submitted 2026-03-26 math.PR math-phmath.CAmath.MP

Donggeun Ryou , Ville Suomala This is my paper · ORCID

classification math.PRmath-phmath.CAmath.MP

keywords dimensioncascadescurvesfouriermandelbrotplanarconsidercurvature

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abstract

We consider multifractal Mandelbrot cascades supported on planar $C^2$ curves with nonvanishing curvature and show that their Fourier dimension is as large as possible, i.e., equal to the infimum of the lower pointwise dimension of the measure.

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