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arXiv · 1611.00462

Endpoint resolvent estimates for compact Riemannian manifolds

Rupert L. Frank·Lukas Schimmer
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Abstract

We prove $L^p\to L^{p'}$ bounds for the resolvent of the Laplace-Beltrami operator on a compact Riemannian manifold of dimension $n$ in the endpoint case $p=2(n+1)/(n+3)$. It has the same behavior with respect to the spectral parameter $z$ as its Euclidean analogue, due to Kenig-Ruiz-Sogge, provided a parabolic neighborhood of the positive half-line is removed. This is region is optimal, for instance, in the case of a sphere.

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Rupert L. Frank, Lukas Schimmer. 2016-11-02. Endpoint resolvent estimates for compact Riemannian manifolds. https://arxiv.org/abs/1611.00462

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