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C = {(x, y, z) : (x, y) ∈ D, λ < z < f(x, y)}
Area(D) = 12π
2π
2Volume(C) := 2
Φ(S, F ) = 12π − √ 12 Area(L) + 2Volume(C).
= 2
= 2
= 2
= 2
√ 12 f(r cos θ,r sin θ)
0 0 0
2π √ 12 f(r cos θ,r sin θ)
0 0
2π √ 12
0 0
√ 12 2π
0 0
√ 12 2π
0
0
λ
r dθdr
r dz dθ dr
r(f(r cos θ, r sin θ) − λ) dθ dr
(r 3 cos θ sin θ − rλ) dθ dr
r 3 cos θ sin θ dθ dr − 2λπ
√ 12
0
r dr = −24λπ,
λ < 0 L ψ1(θ, z) = ( √ 12 cos θ, √ 12 sin θ, z)
⎛
Jac ψ1(θ, z) = ⎝ −√ ⎞
12 sin θ
√
0
0 12 cos θ ⎠ .
0 1
ω2 =
=
det 2
− √ 12 sin θ 0
0 1
12 sin 2 θ + 12 cos 2 θ = √ 12.
+ det 2
√
12 cos θ 0
0 1
+ det 2
√
−
√
12 sin θ 0
12 cos θ 0