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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
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