# Questions tagged [minimal-surfaces]

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

275 questions
Filter by
Sorted by
Tagged with
20 views

### asymptotic directions are perpendicular then the mean curvature is zero?

I just did exercise 7 from Manfredo's section 3.2, which says that if the mean curvature is zero at a non-planar point then the asymptotic directions are perpendicular. My question is: Is the converse ...
26 views

1 vote
86 views

### How can the boundary of a Riemannian $3$-manifold consist of minimal surfaces?

I'm studying a research paper, and there is a theorem whose statement looks very strange to me. In 2001, Gerhard Huisken and Tom Ilmanen proposed a theorem in their collaborative work THE INVERSE MEAN ...
33 views

### Energy Function Expansion in Deform by Laplacian Coordinates

I am currently working on the strain energy function for a particular graph. The paper I am currently referencing is "Spatial Relations Preserving Character Motion Adaptation". I am asking ...
1 vote
50 views

### reference on minimal surfaces

I'm looking for an existence theorem of minimal surface. In a paper by L. Andersson and J Metzger, 'The Area of Horizons and the Trapped Region', they used Jang's equaiton to prove existence of stable ...
63 views

1 vote
36 views

### 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 ...
103 views

### 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 ...
37 views

### 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 ...
59 views

### 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 $\omega_1, \omega_2 \ T_p(S)$ ...
1 vote