Shusen Yang — Neckpinchhttps://neckpinch.com/authors/shusen-yang/New arXiv papers by Shusen Yang, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT Eigenvalues of the Laplace operator with potential under the backward Ricci flow on locally homogeneous 3-manifoldshttps://neckpinch.com/papers/2101.12464/arxiv:2101.12464Fri, 29 Jan 2021 00:00:00 GMTSongbo Hou, Shusen Yang — Let λ(t) be the first eigenvalue of −Δ+aR (a>0) under the backward Ricci flow on locally homogeneous 3-manifolds, where R is the scalar curvature. In the Bianchi case, we get the upper and lower bounds of λ(t). In particular, we show that when the the backward Ricci flow converges to a sub-Riemannian geometry after a proper re-scaling, λ⁺(t) approaches zero, where λ⁺(t)=max\λ(t),0\.Ricci flow3-manifoldsScalar curvatureHomogeneous spacesEigenvalues & spectrum