Abstract
We prove lower bounds for the length of the zero set of aneigenfunction of the Laplace operator on a Riemann surface; inparticular, in non-negative curvature, or when the associated eigenvalueis large, we give a lower bound which involves only the square root ofthe eigenvalue and the area of the manifold (modulo a numericalconstant, this lower bound is sharp).
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Savo, A. Lower Bounds for the Nodal Length of Eigenfunctions of the Laplacian. Annals of Global Analysis and Geometry 19, 133–151 (2001). https://doi.org/10.1023/A:1010774905973
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DOI: https://doi.org/10.1023/A:1010774905973