Critical sets of eigenfunctions of the Laplacian

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Laurent, Bakri

关键词: Carleman inequalities;    Three balls inequalities;    Doubling estimates;    Laplacian operator;    Nodal sets;    Critical sets;   

DOI  :  10.1016/j.geomphys.2012.05.006

来源: Elsevier

【 摘 要 】

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. (c) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free