Almost sharp lower bound for the nodal volume of harmonic functions

IF 4.3 3区材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC ACS Applied Electronic Materials Pub Date : 2024-05-29 DOI:10.1002/cpa.22207

Alexander Logunov, Lakshmi Priya M. E., Andrea Sartori

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Abstract

This paper focuses on a relation between the growth of harmonic functions and the Hausdorff measure of their zero sets. Let $u$ be a real-valued harmonic function in $R^{n}$ with $u (0) = 0$ and $n \geq 3$ . We prove

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谐函数节点体积的近似尖锐下界

本文主要研究谐函数的增长与其零集的 Hausdorff 度量之间的关系。设是一个实值谐函数，且。我们证明了翻倍指数是由定义的增长概念，这给出了、的零集的 Hausdorff 度量的一个近乎尖锐的下限，猜想它是线性的。文章的新内容是稳定增长的概念，以及谐函数倍指数分布下界的多尺度归纳技术。与之前最著名的下界，即纳迪拉什维利猜想相比，它给出了一个重大改进。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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