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Classical two-dimensional Liouville gravity is often considered in conformal gauge which has a residual left and right Virasoro symmetry algebra. We consider an alternate, chiral, gauge which has a residual right Virasoro Kac-Moody algebra, and no left Virasoro algebra. The Kac-Moody zero mode is the left-moving energy. Dirac brackets of the constrained Hamiltonian theory are derived, and the residual symmetries are shown to be generated by integrals of the conserved chiral currents. The central charge and Kac-Moody level are computed. The possible existence of a corresponding quantum theory is discussed.

We consider a characteristic problem of the vacuum Einstein equations with part of the initial data given on a future asymptotically flat null cone, and show that the solution exists uniformly around the null cone for general such initial data. Therefore, the solution contains a piece of the future null infinity. The initial data are not required to be small and the decaying condition is consistent with those in the works of [8] and [11].