2019/01/03 by Xiaoli Han, Han, Xiaoli, Lei Liu +4
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1901.00901
openalex publication_date 2019/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We investigate a parabolic-elliptic system for maps (u,v) from a compact Riemann surface M into a Lorentzian manifold N×ℝ with a warped product metric. That system turns the harmonic map type equations into a parabolic system, but keeps the v-equation as a nonlinear second order constraint along the flow. We prove a global existence result of the parabolic-elliptic system by assuming either some geometric conditions on the target Lorentzian manifold or small energy of the initial maps. The result implies the existence of a Lorentzian harmonic map in a given homotopy class with fixed boundary data.