标题： 梯度 Ricci 溶解中常加权平均曲率超曲面的$f$稳定性指数 显示英文标题

标题： The $f$-Stability Index of the Constant Weighted Mean Curvature Hypersurfaces in Gradient Ricci Solitons

摘要： 在本文中，我们证明了一个具有有限加权体积、加权平均曲率向量在范数上被限制，并且等距浸入到一个完备加权流形中的非紧致完备超曲面是正规的。 此外，我们得到了一个常数加权平均曲率超曲面的$f$-稳定性指标估计，该超曲面具有有限加权体积，并且等距浸入到一个接受至少一个全局定义的平行场的收缩梯度 Ricci 溶解中。 对于这样的超曲面，我们仍然给出了在所得估计中等式成立的必要条件。 显示英文摘要

摘要： In this paper, we prove that a noncompact complete hypersurface with finite weighted volume, weighted mean curvature vector bounded in norm, and isometrically immersed in a complete weighted manifold is proper. In addition, we obtain an estimate for $f$-stability index of a constant weighted mean curvature hypersurface with finite weighted volume and isometrically immersed in a shrinking gradient Ricci soliton that admits at least one parallel field globally defined. For such hypersurface, we still give a necessary condition for equality to be achieved in the estimate obtained.