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Average $L^q$ growth and nodal sets of eigenfunctions of the Laplacian on surfaces
| Content Provider | Semantic Scholar |
|---|---|
| Author | Roy-Fortin, Guillaume |
| Copyright Year | 2015 |
| Abstract | In a recent paper, we exhibit a link between the average local growth of Laplace eigenfunctions on surfaces and the size of their nodal set. In that paper, the average local growth is computed using the uniform - or $L^\infty$ - growth exponents on disks of wavelength radius. The purpose of this note is to prove similar results for a broader class of $L^q$ growth exponents with $q \in (1, \infty)$. More precisely, we show that the size of the nodal set is bounded above and below by the product of the average local $L^q$ growth with the frequency. We briefly discuss the relation between this new result and Yau's conjecture on the size of nodal sets. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1510.02376v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
