摘要
Let (M,g) and (N,h)be two Riemannian manifolds. Consider the heat flow for harmonic maps from (M,g) into (N,h).We prove the following results Suppose dim M =3 and is a nontrivial homotopy class in C(M,N).Then there exists a constant ?o such that if and E(u0)<e, the solution of the heat flow with initial value u0 must blow up in finite time. We also present a sufficient condition which ensures that any global solutions subconverge to harmonic maps as t→∞.
Let (M,g) and (N,h)be two Riemannian manifolds. Consider the heat flow for harmonic maps from (M,g) into (N,h).We prove the following results Suppose dim M =3 and is a nontrivial homotopy class in C(M,N).Then there exists a constant ?o such that if and E(u0)<e, the solution of the heat flow with initial value u0 must blow up in finite time. We also present a sufficient condition which ensures that any global solutions subconverge to harmonic maps as t→∞.
出处
《数学进展》
CSCD
北大核心
1990年第1期80-92,共13页
Advances in Mathematics（China）
