论文标题
光谱多重性和淋巴结集，用于通用圆环不变的指标
Spectral multiplicity and nodal sets for generic torus-invariant metrics
论文作者
论文摘要
让torus $ t $至少在封闭的$ m $上自由起作用至少两个。我们证明，对于$ m $上的普通$ t $ invariant riemannian公制$ g $，每个真正的$Δ_g$ -eigenspace是$ t $的不可约的真实表示，因此最多有两个。我们还表明，对于$ m $上的通用$ t $ invariant公制，如果$ u $是一种无变种的真实价值$Δ_g$ - eigenfunction，它消失在一些$ t $ -orbit上，则$ u $ $ u $的节点是一种相互连接的相互连接的组合，具有两个连接的组合。
Let a torus $T$ act freely on a closed manifold $M$ of dimension at least two. We demonstrate that, for a generic $T$-invariant Riemannian metric $g$ on $M$, each real $Δ_g$-eigenspace is an irreducible real representation of $T$ and, therefore, has dimension at most two. We also show that, for the generic $T$-invariant metric on $M$, if $u$ is a non-invariant real-valued $Δ_g$-eigenfunction that vanishes on some $T$-orbit, then the nodal set of $u$ is a connected smooth hypersurface whose complement has exactly two connected components.
