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 non-negative 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).
Lower bounds for the nodal length of eigenfunctions of the Laplacian / Savo, Alessandro. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - STAMPA. - 19:2(2001), pp. 133-151. [10.1023/a:1010774905973]
Lower bounds for the nodal length of eigenfunctions of the Laplacian
SAVO, Alessandro
2001
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 non-negative 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).File allegati a questo prodotto
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