Isoparametric foliations and critical sets of eigenfunctions

DOI10.1007/S00209-016-1798-3zbMATH Open1384.53055arXiv1203.2089OpenAlexW2537935998MaRDI QIDQ2406022

Author name not available (Why is that?)

Publication date: 26 September 2017

Published in: (Search for Journal in Brave)

Abstract: Jakobson and Nadirashvili cite{JN} constructed a sequence of eigenfunctions on $T^2$ with a bounded number of critical points, answering in the negative the question raised by Yau cite{Yau1} which asks that whether the number of the critical points of eigenfunctions for the Laplacian increases with the corresponding eigenvalues. The present paper finds three interesting eigenfunctions on the minimal isoparametric hypersurface $M^n$ in $S^{n+1}(1)$. The corresponding eigenvalues are $n$, $2n$ and $3n$, while their critical sets consist of $8$ points, a submanifold(infinite many points) and $8$ points, respectively. On one of its focal submanifolds, a similar phenomenon occurs.

Full work available at URL: https://arxiv.org/abs/1203.2089

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Isoparametric foliations and critical sets of eigenfunctions

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2406022)