Submanifolds with parallel weighted mean curvature vector in the Gaussian space (Q2140608)

The authors establish a maximum principle for the drift Laplacian, similar to that one in [\textit{S. Nishikawa}, Nagoya Math.\ J. 95, 117--124 (1984; Zbl 0544.53050)]. Applying it, ``under a suitable boundedness of the second fundamental form'', they ``prove that the hyperplanes are the only complete \(n\)-dimensional submanifolds immersed with either parallel weighted mean curvature vector, for codimension \(p\ge 2\), or constant weighted mean curvature, for codimension \(p=1\), in the \((n+p)\)-dimensional Gaussian space \({\mathbb G}^{n+p}\), which corresponds to the Euclidean space \({\mathbb R}^{n+p}\) endowed with the Gaussian probability measure \(d\mu=e^{-|x|^2/4}d\sigma\), where \(d\sigma\) is the standard Lebesgue measure of \({\mathbb R}^{n+p}\). Furthermore, the authors also use a maximum principle at infinity to get additional rigidity results, as well as a nonexistence result related to nonminimal submanifolds immersed with parallel weighted mean curvature vector in \({\mathbb G}^{n+p}\).'', as they mention in their abstract.