 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-105/1/b/v/solution

For

ϕ (x) = ∣ x ∣^{2} - 1

, the conormal on the unit sphere is

d ϕ = (0, 2 x)

. Hence

p (d ϕ) = 4∣ x ∣^{2} = 4

on the sphere. It is non-characteristic at every point.

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