# Questions tagged [minimal-surfaces]

Question on minimal surfaces, or surfaces that have zero mean curvature.

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### Help understanding smoothness classes. What exactly are the conditions to be a twice continuously differentiable, closed surface?

I know that a $C^2$ surface means the 2nd partial derivatives exist and are smooth, but I'm a bit unfamiliar with math notation/colloquia. I want to make sure I understand correctly. Say we have an ...
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### Inequality regarding minimal perimeter sets

My professor was teaching out of Connor Mooney's notes on Minimal Surfaces and I missed a couple classes and am trying to catch up and I am having trouble understanding the proof of theorem 5.12 (...
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### Gauss Bonnet for locally outermost closed minimal surface in Hawkings Theorem

So I'm trying to understand the proof for the following theorem from Lan-Hsuan Huang: "Trapped Surfaces, Topology of Black Holes, and the Positive Mass Theorem": Any orientable locally ...
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### Bounding diameter of the arc of a closed curve

I was reading chapter 4 of Colding and Minicozzi's A Course in Minimal surfaces and I came across a statement in the proof of Lemma 4.14: Suppose $\Gamma\subset\mathbb{R}^3$ is a simple closed curve ...
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### Continuity of the curve shortening process

I'm studying the shortening process, introduced in the book Course in Minimal Surfaces by T. Colding and W. Minicozzi, which is inspired by the Birkhoff's curve shortening process. In the book, is ...
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### Minimal surface and Gauss map

I am struggling for an exercice in differential geometry : S is a minimal surface if and only if the Gauss map $N : S \rightarrow S^2$ satisfies for all $p \in S$ and all $\omega_1, \omega_2 \ T_p(S)$ ...
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### Using the Divergence theorem to show that a graph has least area among all surfaces with the same boundary

$\DeclareMathOperator{\graph}{graph}$I want to show that for $\Omega\subset\mathbb{R}^2$ an open bounded regular domain with a $C^2$ function $u:\overline{\Omega}\to\mathbb{R}$ that the graph \$\graph(...
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