郭晓东 坐在角落里的人成为主角

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A solution requires solving the hardest known problems in the universe, often requiring years (if not decades) of effort

Fri, 20 Feb 2026 20:32:04 UTC (381 KB)

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Each point \(p \in \mathbb{H}^n\) has tangent vectors \(\frac{\partial}{\partial x^i} in T_p M\) (which we write as the partial derivatives) at \(p\) given local coordinates (i.e. a basis \(\text{span}\{x^1,\dots,x^n\} = T_p M\)). The collection \(\bigl\{\frac{\partial}{\partial x^1}\big|_p,\dots,\frac{\partial}{\partial x^n}\big|_p\bigr\}\) forms a basis of \(T_pM\).

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