Almost sharp lower bound for the nodal volume of harmonic functions

IF 4.3 3区 材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC
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 $u$ be a real-valued harmonic function in R n $\mathbb {R}^n$ with u ( 0 ) = 0 $u(0)=0$ and n 3 $n\ge 3$ . We prove

Abstract Image

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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来源期刊
CiteScore
7.20
自引率
4.30%
发文量
567
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