Almost sharp lower bound for the nodal volume of harmonic functions-Reference-Cited by-同舟云学术

Almost sharp lower bound for the nodal volume of harmonic functions

Published:2024-05-29 Issue: Volume: Page:
ISSN:0010-3640
Container-title:Communications on Pure and Applied Mathematics
language:en
Short-container-title:Comm Pure Appl Math

Author:

Logunov Alexander¹²,Priya M. E. Lakshmi³,Sartori Andrea³

Affiliation:

1. Department of Mathematics Massachusetts Institute of Technology Cambridge Massachusetts USA

2. Section de Mathématiques Université de Genève Geneva Switzerland

3. School of Mathematical Sciences Tel Aviv University Tel Aviv Israel

Abstract

AbstractThis paper focuses on a relation between the growth of harmonic functions and the Hausdorff measure of their zero sets. Let be a real‐valued harmonic function in with and . We prove where the doubling index is a notion of growth defined by This gives an almost sharp lower bound for the Hausdorff measure of the zero set of , which is conjectured to be linear in . The new ingredients of the article are the notion of stable growth, and a multiscale induction technique for a lower bound for the distribution of the doubling index of harmonic functions. It gives a significant imuprovement over the previous best‐known bound , which implied Nadirashvili's conjecture.

Funder

European Research Council

Israel Science Foundation

Barth Syndrome Foundation

Publisher

Wiley

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/cpa.22207

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