摘要
A surface E is a graph in R^4 if there is a unit constant 2-form ω on R^4 such that <e_1∧e_2.ω>≥v_0>0 where{e_1.e_2}is an orthonormal frame on Σ.We prove that.if v_0≥on the initial snrface,then the mean curvature flow has a global solution and the scaled surfaces converge to a self-similar solution.A surface Σ is a graph in M_1×M_2 where M_1 and M_2 are Riemann surfaces. if<e_1∧e_2.ω>≥v_0>0 where w_1 is a Khler form on M_1.We prove that.if M is a Khler-Einstein surface with scalar curvature R.v_0≥ on the initial surface,then the mean curvature flow has a global solution and it sub-converges to a minimal surface,if.in addition.R≥0 it converges to a totally geodesic surface which is holomorphic.
A surface E is a graph in R^4 if there is a unit constant 2-form ω on R^4 such that <e_1∧e_2.ω>≥v_0>0 where{e_1.e_2}is an orthonormal frame on Σ.We prove that.if v_0≥on the initial snrface,then the mean curvature flow has a global solution and the scaled surfaces converge to a self-similar solution.A surface Σ is a graph in M_1×M_2 where M_1 and M_2 are Riemann surfaces. if<e_1∧e_2.ω>≥v_0>0 where w_1 is a Khler form on M_1.We prove that.if M is a Khler-Einstein surface with scalar curvature R.v_0≥ on the initial surface,then the mean curvature flow has a global solution and it sub-converges to a minimal surface,if.in addition.R≥0 it converges to a totally geodesic surface which is holomorphic.
基金
supported in part by a Sloan fellowship and an NSERC grant for Chen
by a grant from NSF of China for Li.by a grant from NSF of USA for Tian
