Perelman singular manifolds

Márcio Batista; Allan Freitas; Márcio Santos

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arXiv · 2404.09369

Perelman singular manifolds

Márcio Batista·Allan Freitas·Márcio Santos

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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 $\delta\mathcal{R}^*$. A manifold endowed with a metric $g$ whose operator $\delta\mathcal{R}^*$ 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.

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Márcio Batista, Allan Freitas, Márcio Santos. 2024-04-14. Perelman singular manifolds. https://arxiv.org/abs/2404.09369

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