Lower Bounds for the Nodal Length of Eigenfunctions of the Laplacian |
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Authors: | Alessandro Savo |
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Affiliation: | (1) Dipartimento di Metodi e Modelli Matematici, Università di Roma `La Sapienza', Via Antonio Scarpa 16, 00161 Rome, Italy |
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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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Keywords: | eigenfunctions Laplace operator nodal sets Riemann surfaces |
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