## Lower bounds for the nodal length of eigenfunctions of the Laplacian.(English)Zbl 1010.58025

Authors’s abstract: We prove lower bounds for the length of the zero set of an eigenfunction of the Laplace operator on a Riemann surface: in particular, in nonnegative curvature, or when the associated eigenvalue is large, we give a lower bound which involves only the square root of the eigenvalue and the area of the manifold (modulo a numerical constant, this lower bound is sharp).

### MSC:

 58J50 Spectral problems; spectral geometry; scattering theory on manifolds

### Keywords:

eigenfunctions of the Laplacian
Full Text: