On Kakeya-Nikodym averages, $L^p$-norms and lower bounds for nodal sets of eigenfunctions in higher dimensions

Matthew D. Blair, Christopher D. Sogge

We extend a result of the second author \cite[Theorem 1.1]{soggekaknik} to dimensions $d\ge 3$ which relates the size of $L^p$-norms of eigenfunctions for $2<p<\frac{2(d+1)}{d-1}…