A Note on Almost Everywhere Convergence Along Tangential Curves to the Schr\"odinger Equation Initial Datum

In this short note, we give an easy proof of the following result: for $n\geq 2,$ $\underset{t\to0}{\lim} \,e^{it\Delta }f\left(x+\gamma(t)\right) = f(x)$ almost everywhere whenever $\gamma$ is an $\alpha-$H\"older curve with $\frac12\leq \alpha\leq 1$ and $f\in H^s(\mathbb{R}^n)$, with $s > \frac{n}{2(n+1)}$. This is the optimal range of regularity up to the endpoint.