A geometric perspective on the method of descent (Q1650150)

This paper concerns the wave equation on a \((2+1)\) globally hyperbolic, smooth Lorentzian spacetime \((M, g)\). The approach is based on the relationship between the geometry of the null cones with the vertex \(p\) in \((3+1)\) spacetime and the causal past of the same vertex in \((2+1)\) spacetime. By uncovering the quantitative correspondence between connection coefficients of the null frames in \((3+1)\) spacetime and those of the triads in \((2+1)\) spacetime the null radius of injectivity is controlled by the causal radius of injectivity. The main result reduces in the flat case to the Poisson formula in Minkowski space.