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In this note we analyse $L^{p}$ estimates for Laplacian eigenfunctions andquasimodes and their associated sharp examples. In particular we use previouslydetermined estimates to produce a new set of estimates for restriction tothickened neighbourhoods of submanifolds. In addition we produce a family flatmodel quasimode examples that can be used to determine sharpness of estimateson Laplacian eigenfunctions restricted to subsets. For each quasimode in thefamily we show that there is a corresponding spherical harmonic that displaysthe same growth properties. Therefore it is enough to check $L^{p}$ growthestimates against the simple flat model examples. Finally we present aheuristic that for any subset determines which quasimode in the family isexpected to produce sharp examples.

A note on constructing sharp examples for $L^{p}$ norms of eigenfunctions and quasimodes near submanifolds