Rigidity for pp-Laplacian type equations on compact Riemannian manifolds

In this paper, we obtain two rigidity results for $p$-Laplacian type equations on compact Riemannian manifolds by using of the carr\'e du champ and nonlinear flow methods, respectively, where rigidity means that the PDE has only constant solution when a parameter is in a certain range. Moreover, an interpolation inequality is derived as an application.Comment: 14 page

A Universal Constraint on the Infrared Behavior of the Ghost Propagator in QCD

With proposing a unified description of the fields variation at the level of generating functional, we obtain a new identity for the quark-gluon interaction vertex based on gauge symmetry, which is similar to the Slavnov-Taylor Identities(STIs) based on the Becchi-Rouet-Stora-Tyutin transformation. With these identities, we find that in Landau gauge, the dressing function of the ghost propagator approaches to a constant as its momentum goes to zero, which provides a strong constraint on the infrared behaviour of ghost propagator.Comment: 4 pages, no figur