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• W2019921075 abstract "The paper deals with asymptotic nodal geometry for the Laplace-Beltrami operator on closed surfaces. Given an eigenfunction f corresponding to a large eigenvalue, we study local asymmetry of the distribution of sign(f) with respect to the surface area. It is measured as follows: take any disc centered at the nodal line {f = 0}, and pick at random a point in this disc. What is the probability that the function assumes a positive value at the chosen point? We show that this quantity may decay logarithmically as the eigenvalue goes to infinity, but never faster than that. In other words, only a mild local asymmetry may appear. The proof combines methods due to Donnelly-Fefferman and Nadirashvili with a new result on harmonic functions in the unit disc." @default.
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• W2019921075 date "2005-01-01" @default.
• W2019921075 modified "2023-10-17" @default.
• W2019921075 title "Sign and area in nodal geometry of Laplace eigenfunctions" @default.
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• W2019921075 doi "https://doi.org/10.1353/ajm.2005.0030" @default.
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