Differential geometry is the application of differential calculus in the setting of smooth manifolds (curves, surfaces and higher dimensional examples). Modern differential geometry focuses "geometric structures" on such manifolds, such as bundles and connections; for questions not concerning such ...

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Complex submanifold has the minimal volume

I know that the following theorem is true: If $W$ is a purely $k$-dimensional analytic subvariety of a domain in $\mathbb{C}^n$, $sngW$ is the set of its singular points, $V \subset W$ is open, ...
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Hausdorff measure, volume form, reference

Could you tell me where I can find a reference to the fourth corollary in this encyclopedia? Corollary $4$: Assume that $\Sigma \subset \mathbb{R}^m$ is an $n$-dimensional $C^1$ ...
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A regular surface with non zero mean curvature is orientable

How can I prove that any regular surface with non zero mean curvature is orientable? UPDATE: The surface is embedded in $\mathbb{R}^3$.