 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2007/ii/paper-2/24h/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

H = (k_{1} + k_{2}) /2

; equivalently its area is stationary under compactly supported normal variations. Its principal curvatures satisfy

k_{2} = - k_{1}

K = k_{1} k_{2} = - k_{1}^{2} \leq 0.

Equality occurs precisely where its second fundamental form vanishes.

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