In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation（δ2 gij）/δt2＋μ/（（1 ＋ t）λ）（δ gij）/δt=-2 Rij,on Riemann surface. On the basis of the energy method, for 0 〈 λ...In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation（δ2 gij）/δt2＋μ/（（1 ＋ t）λ）（δ gij）/δt=-2 Rij,on Riemann surface. On the basis of the energy method, for 0 〈 λ ≤ 1, μ 〉 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.展开更多
In this article, we investigate the lower bound of life-span of classical solutions of the hyperbolic geometry flow equations in several space dimensions with ＂small＂ initial data. We first present some estimates on...In this article, we investigate the lower bound of life-span of classical solutions of the hyperbolic geometry flow equations in several space dimensions with ＂small＂ initial data. We first present some estimates on solutions of linear wave equations in several space variables. Then, we derive a lower bound of the life-span of the classical solutions to the equations with ＂small＂ initial data.展开更多
基金supported in part by the NNSF of China(11271323,91330105)the Zhejiang Provincial Natural Science Foundation of China(LZ13A010002)the Science Foundation in Higher Education of Henan(18A110036)
文摘In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation（δ2 gij）/δt2＋μ/（（1 ＋ t）λ）（δ gij）/δt=-2 Rij,on Riemann surface. On the basis of the energy method, for 0 〈 λ ≤ 1, μ 〉 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.
基金supported in part by the NNSF of China(11271323,91330105)the Zhejiang Provincial Natural Science Foundation of China(LZ13A010002)the Henan Provincial Natural Science Foundation of China(152300410226)
文摘In this article, we investigate the lower bound of life-span of classical solutions of the hyperbolic geometry flow equations in several space dimensions with ＂small＂ initial data. We first present some estimates on solutions of linear wave equations in several space variables. Then, we derive a lower bound of the life-span of the classical solutions to the equations with ＂small＂ initial data.
