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arXiv · 2308.07182

Ends of shrinking gradient $\rho$-Einstein solitons

Valter Borges·Hector Rosero-García·João Paulo dos Santos
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Abstract

We prove that all ends of a gradient shrinking $\rho$-Einstein soliton are $\varphi$-non-parabolic, provided $\rho$ is nonnegative and the soliton has bounded and nonnegative scalar curvature, where the weight $\varphi$ is a negative multiple of the potential function. We also show these solitons are connected at infinity for $\rho \in\left[0,1/2(n-1)\right)$, $n\geq4$, and a suitable bound for the scalar curvature.

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Valter Borges, Hector Rosero-García, João Paulo dos Santos. 2023-08-14. Ends of shrinking gradient $\rho$-Einstein solitons. https://arxiv.org/abs/2308.07182

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