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