LAUSR

Abstract In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation ∂ 2 g i j ∂ t 2 + μ ( 1 + t ) λ ∂ g i j ∂ t = - 2 R i j , on Riemann surface. On the basis of the energy method, for 0 λ + 1, we show that there exists a global solution gij to the hyperbolic geometry flow with time-dependent dissipation with asymptotic flat initial Riemann surfaces. Moreover, we prove that the scalar curvature R(t,x) of the solution metric gij remains uniformly bounded.