Let A, B be two sets and f: A→ B amap. The iterates fn: An→ B,n = 1,2,... Aredefined inductively by
A1 = A, f1 = f and
An = f-1(An-1 ∩ B), fn = fn-1(f) for n ≥ 2.
Note that A2 = f-1(A1 ∩ B) A = A1 and thus An An-...Let A, B be two sets and f: A→ B amap. The iterates fn: An→ B,n = 1,2,... Aredefined inductively by
A1 = A, f1 = f and
An = f-1(An-1 ∩ B), fn = fn-1(f) for n ≥ 2.
Note that A2 = f-1(A1 ∩ B) A = A1 and thus An An-1 A for n ≥ 2.展开更多
<正> Let M be a smooth, compact (closed and without boundary) surface. Consider the metricsσ(z)|dz|~2 and ρ(ω)|dω|~2 on M, where z=x+iy and ω=u+iv are conformal coordinates onM. For a Lipschitz map ω=ω(z)...<正> Let M be a smooth, compact (closed and without boundary) surface. Consider the metricsσ(z)|dz|~2 and ρ(ω)|dω|~2 on M, where z=x+iy and ω=u+iv are conformal coordinates onM. For a Lipschitz map ω=ω(z): (M, σ|dz|~2)→(M, ρ|dw|~2), we define the energy density展开更多
基金Supported partly by the National Natural Science Foundation of China(No.10371078)and the Natural Science Foundation of Guangdong Province in China(No.984112)
文摘Let A, B be two sets and f: A→ B amap. The iterates fn: An→ B,n = 1,2,... Aredefined inductively by
A1 = A, f1 = f and
An = f-1(An-1 ∩ B), fn = fn-1(f) for n ≥ 2.
Note that A2 = f-1(A1 ∩ B) A = A1 and thus An An-1 A for n ≥ 2.
基金Supported partly by the National Natural Science Foundation of China(No.19801024)the Natural Science Foundation of Guangdong Province in China(No.984112)
文摘<正> Let M be a smooth, compact (closed and without boundary) surface. Consider the metricsσ(z)|dz|~2 and ρ(ω)|dω|~2 on M, where z=x+iy and ω=u+iv are conformal coordinates onM. For a Lipschitz map ω=ω(z): (M, σ|dz|~2)→(M, ρ|dw|~2), we define the energy density
