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Normal-Direction Energy and Fourier Restriction for Convex Planar Curves
We study Fourier extension from compact convex $C^2$ planar curves by organizing the mass $|f|^2\,\mathrm dσ$ through the Gauss map. The pushforward measure \[ ν_f= N_\#\bigl(|f|^2\,\mathrm dσ\bigr) \] records its distribution in normal directions. The turning measure $\mathrm dμ_κ=κ\,\mathrm dσ$ de
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