论文标题
在有限的投影家庭下的套件长度
Length of sets under restricted families of projections onto lines
论文作者
论文摘要
令$γ：i \ to s^2 $为$ c^2 $曲线，$ \ det（γ，γ'，γ''）$ nonvanishing，对于i $ let $ρ_θ$中的每个$θ\，对于$γ（θ）$的span of promental profaction。结果表明，如果$ a \ subseteq \ mathbb {r}^3 $是一组Hausdorff尺寸的鲍尔，则严格大于1，则$ρ_θ（a）$的长度为A.E。 $θ\ in I $。这回答了Käenmäki，Orponen和Venieri提出的一个问题。
Let $γ: I \to S^2$ be a $C^2$ curve with $\det(γ, γ', γ'')$ nonvanishing, and for each $θ\in I$ let $ρ_θ$ be orthogonal projection onto the span of $γ(θ)$. It is shown that if $A \subseteq \mathbb{R}^3$ is a Borel set of Hausdorff dimension strictly greater than 1, then $ρ_θ(A)$ has positive length for a.e. $θ\in I$. This answers a question raised by Käenmäki, Orponen and Venieri.
