Changkeun Oh

Positive measure for restricted projections along smooth non-degenerate curves

Let $1\leq m<n$, and let $\gamma:[0,1]\to\mathbb R^n$ be a smooth non-degenerate curve. For $\theta\in[0,1]$, set \[ V_\theta := \operatorname{span} \{\gamma'(\theta),\ldots,\gamma^{(m)}(\theta)\}, \] and let $\pi_\theta$ denote the orthogonal projection onto $V_\theta$. We prove that if $E\subset\mathbb R^n$ is a Bore...