In this paper we establish a natural framework for the stability of mean curvature flow solitons in warped product spaces. These solitons are regarded as stationary immersions for a weighted volume functional. Under this point of view, we are able to find geometric conditions for finiteness of the index and some characterizations of stable solitons. We also prove some non-existence results for solitons as applications of a comparison principle which suits well the structure of the diffusion elliptic operator associated to the weighted measures we are considering.

中文翻译：

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翘曲积空间中平均曲率流孤子的稳定性

在本文中，我们为扭曲产品空间中的平均曲率流孤子的稳定性建立了一个自然的框架。这些孤子被认为是加权体积功能的固定浸入。根据这种观点，我们能够找到指数有限性和稳定孤子的某些表征的几何条件。作为比较原理的应用，我们还证明了孤子的一些不存在的结果，该原理非常适合与我们正在考虑的加权度量相关联的扩散椭圆算子的结构。