In this paper, for the Lorentz manifold M^(2)× R with M^(2) a 2-dimensional complete surface with nonnegative Gaussian curvature, the authors investigate its spacelike graphs over compact, strictly convex domains in M^(2), which are evolving by the nonparametric mean curvature flow with prescribed contact angle boundary condition, and show that solutions converge to ones moving only by translation.
In this paper, the Almgren's frequency function of the following sub-elliptic equation with singular potential on the Heisenberg group:—Lu + V(z, t)u = Xi (aij (z, t)Xju) + V(z,t)u = 0 is introduced. The monotonicity property of the frequency is established and a doubling condition is obtained. Consequently, a quantitative proof of the strong unique continuation property for such equation is given.
