A Flux Formula For Weighted Manifolds

[摘要] In this article, we derive a flux formula in a weighted manifold, using the weighted Newton transformations and introducing the notion of weighted higher order mean curvature, this formula generalizes. Reilly’s original formula and the flux formula obtained by Alias, Lopez and Malcarne [1]. In particular, we obtain a similar balancing formula obtained by Rosenberg. Finally, we give some special cases of our formula.

[关键词] Weighted manifolds;Weighted;Newton transformation;rth mean curvature;Weighted mean curvature