129 citations · 553 across the 62 of their papers we have counts for
8 papers · 1 filter
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…
The Neumann isospectral problem for trapezoids
Hamid Hezari, Zhiqin Lu, Julie Rowlett
We show that trapezoids with identical Neumann spectra are congruent up to rigid motions of the plane. The proof is based on heat trace invariants and some new wave trace invariant…
On the discrete spectrum of quantum layers
Zhiqin Lu, Julie Rowlett
Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, smooth surface embedded in . We assume…
The fundamental gap of simplices
Zhiqin Lu, Julie Rowlett
The fundamental gap conjecture was recently proven by Andrews and Clutterbuck: for any convex domain in normalized to have unit diameter, the difference between the first tw…