Planck-scale number of nodal domains for toral eigenfunctions
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DOI: 10.1016/j.jfa.2020.108663
Abstract: We study the number of nodal domains in balls shrinking slightly above the Planck scale for "generic" toral eigenfunctions. We prove that, up to the natural scaling, the nodal domains count obeys the same asymptotic… read more here.
Keywords: toral eigenfunctions; nodal domains; planck scale; scale number ... See more keywords
Spectral Multiplicity and Nodal Domains of Torus-Invariant Metrics
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DOI: 10.1093/imrn/rnad102
Abstract: Let a $d$-dimensional torus $\mathbb{T}$ act freely and smoothly on a closed manifold $M$ of dimension $n>d$. We show that, for a generic $\mathbb{T}$-invariant Riemannian metric $g$ on $M$, each real $\Delta _{g}$-eigenspace is an… read more here.
Keywords: multiplicity nodal; torus invariant; domains torus; mathbb ... See more keywords