Year: 2024
Type: preprint
Abstract: On a Riemannian manifold with a smooth function $f: M\to \mathbb{R}$, we consider the linearization of the Perelman scalar curvature $\mathcal{R}$ and its $L^2$-formal adjoint operator $δ\mathcal{R}^*$. A manifold endowed with a metric $g$ whose operator $δ\mathcal{R}^*$ has a nontrivial kernel is called a Perelman singular manifold. In this paper, we present examples and apply general maximum principles to obtain rigidity or nonexistence results in the underlying setting.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394866490