$λ$-geodesic convexity of the squared sliced-Wasserstein distance

The squared Wasserstein distance with respect to a fixed target measure is not a convex function along Wasserstein geodesics over $\mathbb{R}^d$ when $d\geq 2$. Still, in dimension $d=1$, this function is $2$-geodesically convex. We prove that the square of the sliced-Wasserstein distance (which is