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

Interference of surface plasmon polaritions controlled by the phase of incident light

Interference patterns of surface plasmon polaritons(SPPs) are observed in the extraordinary optical transmission through subwavelength holes in optically thick metal plate. It is found that the phase of incident light can be transferred to SPPs. We can control the destructive and constructive interference of SPPs by modulating the relative phase between two incident beams. Using a slightly displaced Mach-Zehnder interferometer, we also observe a SPPs interference pattern composed of bright and dark stripes.Comment: 3pages,5figure