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First, we correct the proof presented in [Abimbola Abolarinwa, Kamilu Rauf,Songting Yin, Sharp $L^{p}$ Hardy type and uncertainty principle inequalitieson the sphere, Journal of Mathematical Inequalities, 13, 4 (2019), 1011 - 1022]and obtain a correct sharp version of an $L^{p}$ Hardy inequality on the sphere$\mathbb{S}^{n}$ for all $2\leq p<n$. Secondly, we prove sharp criticalexponent $L^{n}$ inequalities on the sphere $\mathbb{S}^{n}$ in$\mathbb{R}^{n+1}$, $n\geq 2$. The singularity in this problem is the geodesicdistance from an arbitrary point on the sphere.

Optimal critical exponent $L^{p}$ inequalities of Hardy type on the sphere via Xiao's method