2022/11/17 by Gan, Shengwen, Guo, Shaoming, Wang, Hong · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2211.09508
Let γ: [-1, 1]→ ℝn be a smooth curve that is non-degenerate. Take m≤ n and a Borel set E⊂ [0, 1]n. We prove that the orthogonal projection of E to the m-th order tangent space of γ at θ∈ [-1, 1] has Hausdorff dimension min\m, dim(E)\ for almost every θ∈ [-1, 1].