129 citations · 553 across the 62 of their papers we have counts for
64 papers
A note on Cheeger's isoperimetric constant
Nelia Charalambous, Zhiqin Lu
In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric constant.
Connected essential spectrum: the case of differential forms
Nelia Charalambous, Zhiqin Lu
In this article we prove that, over complete manifolds of dimension with vanishing curvature at infinity, the essential spectrum of the Hodge Laplacian on differential -form…
On a Conjecture of Bahri-Xu
Hong Chen, Jianquan Ge, Kai Jia +1
In order to study the Yamabe changing-sign problem, Bahri and Xu proposed a conjecture which is a universal inequality for points in . They have verified the conje…
Eigenvalue Estimates on Bakry-Emery Manifolds
Nelia Charalambous, Zhiqin Lu, Julie Rowlett
We demonstrate lower bounds for the eigenvalues of compact Bakry-Emery manifolds with and without boundary. The lower bounds for the first eigenvalue rely on a generalised maximum…
One can hear the corners of a drum
Zhiqin Lu, Julie Rowlett
We prove that the presence or absence of corners is spectrally determined in the following sense: any simply connected domain with piecewise smooth Lipschitz boundary cannot be iso…
The sound of symmetry
Zhiqin Lu, Julie Rowlett
This note begins with an introduction to the inverse isospectral problem popularized by M. Kac's 1966 article in the American Mathematical Monthly, "Can one hear the shape of a dru…