# Tagged Questions

**0**

votes

**0**answers

104 views

### Third variation of area of a minimal surface

There is a formula for the third variation of area on page 96 of Nitsche's book,
Lectures on Minimal Surfaces, vol. 1 (English version). He says at the bottom of the
page it is good for normal ...

**3**

votes

**3**answers

287 views

### Lagrangian Kleinian bottles

I remember some talks some time ago about proofs of nonexistence of Lagrangian Kleinian bottles in C^2 for the standard symplectic structure, mentioning that this were the only compact surface for ...

**5**

votes

**2**answers

559 views

### Pursuit-Evasion on a Manifold

I know pursuit-evasion has been studied in many contexts, including
on a manifold (e.g., Melikyan,
"Geometry of Pursuit-Evasion Games on Two-Dimensional Manifolds"),
but I have not seen this version:
...

**1**

vote

**4**answers

510 views

### What is the quantity 2(handles)+crosscaps called?

It is well-known that up to homeomorphism, the complete set of orientable surfaces is $\lbrace S_g : g=0,1,\dots \rbrace$, where $S_g$ is the sphere with $g$ handles. The complete set of ...

**15**

votes

**2**answers

912 views

### Simple curves on non-orientable surfaces.

Given an element in the (first) homology group of a surface, I would like to know if it can be represented as a simple closed curve. For orientable surfaces, this is well-known, but I wasn't able to ...

**15**

votes

**5**answers

867 views

### Is a rhombus rigid on a sphere or torus? And generalizations.

If a rectangle is formed from rigid bars for edges and joints
at vertices, then it is flexible in the plane: it can flex
to a parallelogram.
On any smooth surface with a metric, one can define a ...

**3**

votes

**1**answer

222 views

### Removing intersections of curves in surfaces

Let $C_1, \dots, C_n$ be a family of disjoint simple curves in a surface $\Sigma$. If $C$ is any simple curve in $\Sigma$, it turns out that we can map $C$ to a curve $C'$ (via a homeomorphism of ...