Question on minimal surfaces, or surfaces that have zero mean curvature.
Questions tagged [minimal-surfaces]
281 questions
4
votes
3 answers
Given a volumen. Which is the suface, that contains it, that has minimal area?
Defining on $R^3$, $V = \iiint_S dx \, dy \, dz $ as the volume of surface $S$, with $S$ closed, bounded and arc-connected. Which is the $S$ of minimal area, that contains $V$. I know it's a bit general, so maybe you could think of another…
John
- 43
2
votes
1 answer
What is the function describing the minimal surface of this object?
What function describes the minimal surface of this object?
The object consists of four circular arcs glued together. One arc is parallell to another arc, and a third arc is parallell to a fourth arc. The first two arcs are orthogonal to the other…
Mats Granvik
- 7,396
1
vote
0 answers
Seeking a parametrization for the octoid
My undergraduate student and I are working through chapter 2 of the book Complex Analysis Topics for
Undergraduates and Beginning Researchers: an Exploration with Unsolved Problems,…
1
vote
0 answers
Do minimal surfaces imply minimal volume?
I have a set of non-intersecting (approximate) minimal surfaces derived from a parametrization of a gyroid that I've cropped & capped the ends, see image below for 3d print of some of them.
Am I right in assumiing that, in my case, given a minimal…
DrBwts
- 127
1
vote
3 answers
Minimal surface between two parallel circle of same radius : why is it a surface of revolution?
I would like to find a minimal surface between two parallel circle of same radius (i.e. they are coaxial). I in fact just need to know that it's a revolution surface to conclude that it will be a catenoid. So let $\Sigma$ such a surface. How can I…
MSE
- 3,153
1
vote
0 answers
Necessary relation for closed lines on minimal surfaces
Is there a necessary relation between curvature and torsion of a closed non-intersecting curve on a minimal surface?
While playing with soap films I noted closed light threads migrating on a soap film in a certain way difficult to mathematically…
Narasimham
- 40,495
1
vote
1 answer
Scherk’s fifth minimal surface
Scherk’s fifth minimal surface is defined implicitly by
$$
\sin(z)=\sinh(x) \sinh(y).
$$
How can I show that this surface is minimal?
teo
- 166
0
votes
0 answers
A minimal surface
http://en.wikipedia.org/wiki/Minimal_surface
Ref: The first figure with soap film at right.
What is surface parametrization or references? How is it connected to the
helicoid/catenoid ? Thanks.
Narasimham
- 40,495
0
votes
0 answers
Minimal surface stretched over four points
Let $x_0, \ldots, x_3 \in \mathbb{R}^3$. Let $C$ be a pathwise affine curve connecting these points in order $x_0 \to x_1 \to x_2 \to x_3 \to x_0$. (That is, $C$ consists of four segments that connect $x_i$ to $x_{i+1}$ with $x_4 = x_0$). I would…
Kakuro
- 303
0
votes
0 answers
Second fundamental form of minimal surface under Weierstrass representation.
Consider the Weierstrass representation $$f(z)=\text{Re}\int ((1-g^2),i(1+g^2),2g)\omega$$, where $g(z)$ is a meromorphic function and $\omega(z)$ is a holomorphic 1 form.
I'm trying to derive the following expression of second fundamental form…
jlidm
- 187
0
votes
1 answer
Minimal surfaces, how to convert different Enneper-Weierstrass representation?
I don't know much about Enneper-Weierstrass representation, but it seems in general, for a surface, we provide a holomorphic function $f$ and a meromorphic function $g$. For the catenoïd for instance, this would be :
$(f,g) =…
roi_saumon
- 4,196