$df=\frac{\partial f }{\partial x_i}dx^i$ is 1-form. $(~,~)$ is $L^2(M)$ inner. $(M,g)$ is a compact smooth Rie-mfd. How to show 3.1.21. In fact ,I just fail to deal $\partial_i\sqrt{g}$. I don't know how to calculate it .
2026-04-02 20:10:31.1775160631
A calculation of Laplace-Beltrami operator.
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