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- W4377224981 abstract "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 irreducible real representation of $mathbb{T}$ and, therefore, has dimension at most two. We also show that, for the generic $mathbb{T}$-invariant metric $g$ on $M$, if $u$ is a non-invariant real-valued $Delta _{g}$-eigenfunction that vanishes on some $mathbb{T}$-orbit, then the nodal set of $u$ is a connected smooth hypersurface. If $n>d+1$, we show that the complement of the nodal set has exactly two connected components. As a consequence, we obtain new examples of manifolds for which—up to a sequence of Weyl density zero—each eigenfunction has exactly two nodal domains." @default.
- W4377224981 created "2023-05-23" @default.
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- W4377224981 date "2023-05-19" @default.
- W4377224981 modified "2023-09-27" @default.
- W4377224981 title "Spectral Multiplicity and Nodal Domains of Torus-Invariant Metrics" @default.
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- W4377224981 doi "https://doi.org/10.1093/imrn/rnad102" @default.
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