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Critical sets of eigenfunctions of the Laplacian |
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| Authors: | Bakri Laurent |
| Institution: | Laboratoire de Mathématiques et Physique Théorique, Université François Rabelais, Parc de Grandmont, 37200 Tours, France |
| Abstract: | We give an upper bound for the (n−1)-dimensional Hausdorff measure of the critical set of eigenfunctions of the Laplacian on compact analytic n-dimensional Riemannian manifolds. This is the analog of a result on the nodal set of eigenfunctions by H. Donnelly and C. Fefferman. |
| Keywords: | Carleman inequalities Three balls inequalities Doubling estimates Laplacian operator Nodal sets Critical sets |
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