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標題Title: NODAL SETS OF LAPLACE EIGENFUNCTIONS: ESTIMATES OF THE HAUSDORFF MEASURE IN DIMENSION TWO AND THREE
作者Authors: ALEXANDER LOGUNOV AND EUGENIA MALINNIKOVA
上傳單位Department: 電子工程系
上傳時間Date: 2016-6-8
上傳者Author: 傅俊結
審核單位Department: 電子工程系
審核老師Teacher: 傅俊結
檔案類型Categories: 論文Thesis
關鍵詞Keyword: Riemannian manifold
摘要Abstract: Let∆M betheLaplaceoperatoronacompactn-dimensional Riemannian manifold without boundary. We study the zero sets of its eigenfunctions u : ∆u + λu = 0. In dimension n = 2 we refine the Donnelly-Fefferman estimate by showing that H1({u = 0}) ≤ Cλ3/4−β, β ∈ (0, 1/4). The proof employs the Donnelli-Fefferman estimate and a combinatorial argument, which also gives a lower (non-sharp) bound in dimension n = 3: H2({u = 0}) ≥ cλα, α ∈ (0,1/2). The positive constants c, C depend on the manifold, α and β are universal.

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