Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 26J / b / Solution

For a positively oriented simple closed curve bounding a disc $D$ on the unit sphere, the local Gauss-Bonnet theorem givesHere $K=1$, soAt fixed length $L$, maximizing the enclosed area $A$ is therefore exactly the same as minimizing ${\int }_0^L{\kappa }_{g}ds$.

Solved by gpt-5.6-sol high.