On Instability of the Nikodym Maximal Function bounds over Riemannian Manifolds

Christopher D. Sogge, Yakun Xi, Hang Xu

We show that, for odd $d$, the $L^{\frac{d+2}{2}}$ bounds of Sogge and Xi for the Nikodym maximal function over manifolds of constant sectional curvature, are unstable with respect t…