For a compact surface, $S$, in $\mathbb{R}^3$, how would I go about showing that the total Gaussian curvature $\int_S K da \leq 4 \pi$? I feel like Hopf's Umlaufsatz and the Gauss-Bonnet Theorem are helpful.
2026-03-25 23:36:10.1774481770
Total Gaussian curvature
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