Methods and Applications of Analysis

Volume 27 (2020)

Number 4

Special Issue for the 60th Birthday of John Urbas: Part I

Guest Editors: Neil Trudinger and Xu-Jia Wang

A note on nodal sets on manifolds with lower Ricci bound

Pages: 359 – 374

DOI: https://dx.doi.org/10.4310/MAA.2020.v27.n4.a3

Authors

Jianchun Chu (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)

Wenshuai Jiang (School of Mathematical Sciences, Zhejiang University, Hangzhou, China; and School of Mathematics and Statistics, University of Sydney, NSW, Australia)

Abstract

In this note, we study nodal sets of harmonic functions on Riemannian manifolds with lower Ricci curvature bound and the noncollapsing lower volume bound. Both upper and lower bound measure estimates of nodal sets are established.

Keywords

nodal sets, Ricci curvature, noncollapsing

2010 Mathematics Subject Classification

Primary 58J05. Secondary 35J15.

Received 19 March 2020

Accepted 15 July 2020

Published 24 September 2021