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Nodal sets of Laplace eigenfunctions : estimates of the Hausdorff measure in dimensions two and three
| Content Provider | Semantic Scholar |
|---|---|
| Author | Logunov, Alexander Malinnikova, Eugenia |
| Copyright Year | 2019 |
| Abstract | Let ∆M be the Laplace operator on a compact n-dimensional Riemannian manifold without boundary. We study the zero sets of its eigenfunctions u : ∆Mu + λu = 0. In dimension n = 2 we refine the Donnelly-Fefferman estimate by showing that H({u = 0}) ≤ Cλ for some β ∈ (0, 1/4). The proof employs the Donnelly-Fefferman estimate and a combinatorial argument, which also gives a lower (nonsharp) bound in dimension n = 3: H({u = 0}) ≥ cλ for some α ∈ (0, 1/2). The positive constants c, C depend on the manifold, α and β are universal. Mathematics Subject Classification (2010). Primary 31B05; Secondary 35R01, 58G25. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv-export-lb.library.cornell.edu/pdf/1605.02595 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
