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arXiv · 1411.4078

$L^p$ norms, nodal sets, and quantum ergodicity

Hamid Hezari·Gabriel Riviere
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Abstract

For small range of $p>2$, we improve the $L^p$ bounds of eigenfunctions of the Laplacian on negatively curved manifolds. Our improvement is by a power of logarithm for a full density sequence of eigenfunctions. We also derive improvements on the size of the nodal sets. Our proof is based on a quantum ergodicity property of independent interest, which holds for families of symbols supported in balls whose radius shrinks at a logarithmic rate.

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Hamid Hezari, Gabriel Riviere. 2014-11-14. $L^p$ norms, nodal sets, and quantum ergodicity. https://arxiv.org/abs/1411.4078

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