Suppose that Ï{B) and Ï(E) are Cp surfaces and that Ï = Ï o Ï, where Ï

Suppose that ψ{B) and ϕ(E) are Cp surfaces and that ψ = ϕ o τ, where τ is a C1 function from B onto E.
a) If {ψ, B) and (Ï•, E) are smooth, and Ï„ is 1-1 with Δτ > 0 on B, prove for all continuous F: Ï•(E) †’ R3 that

b) Suppose that Z is a closed subset of B of area zero, that (ψ, B) is smooth off Z, and that Ï„ is 1-1 with Δτ > 0 on BoZ. Prove for all continuous F: Ï•(E) †’ R3 that

Transcribed Image Text:

F@cu, u)) . Νφ(u, u) d(u. U) :: | F(ψ (s, t)) . Ny(s, t) d(s, t).