题号:14624    题型:解答题    来源:2024年丘成桐大学生数学竞赛(几何与拓扑类)-无答案
Let $\Sigma \subset \mathbb{R}^3$ be an embedded surface in $\mathbb{R}^3$. A surface is calle $\mathrm{d}$ minimal if, for any $p \in \Sigma$, we have $\kappa_1(p)+\kappa_2(p)=0$, whe re $\kappa_1(p)$ and $\kappa_2(p)$ are the two principal curvatures at $p$. Prov e that if $\Sigma$ is closed, then $\Sigma$ cannot be minimal.
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