# Tagged Questions

**3**

votes

**1**answer

171 views

### Delta-convex functions and inner products

A delta-convex (d.c.) function is one which can be written as the difference of two convex functions.
The space of d.c. functions includes all C2 functions, and is interesting because it allows many ...

**3**

votes

**1**answer

184 views

### Riemannian metric on a space of “not-quite-smooth” (hyper)surfaces?

Apologies if the title's a bit vague; I'll try to explain everything below, and please let me know if I should clarify anything.
I've been looking for a while at variational problems on polytopes. ...

**1**

vote

**1**answer

445 views

### Solutions to Heat Equations with Obstacles!

Consider a closed Riemannian manifold $(M,g)$ and a positive function $\psi: M \to R$. Fix a point $p \in M$, I have been struggling to construct a solution to the heat equation, $\partial_t u = ...

**3**

votes

**1**answer

178 views

### Integral of a quadratic on a polygon (variations of discrete surfaces)

This question is pretty simple to state: given two linear functions on a polygon, I'm looking for a formula for the integral of their product which depends only on the values at the (unlabelled) edges ...

**2**

votes

**0**answers

279 views

### Partial feedback linearization (Control theory)

Greetings,
I'm trying to understand a theorem about partial feedback linearization from a paper "On the largest feedback linearizable subsystem" by R.Marino (you can find it here: ...

**6**

votes

**1**answer

260 views

### Constructing a hypersurface with given outer normals

Pick a point on each of the positive half-axes in $\mathbb{R}^n$. Put a (unit-norm?) vector at each of the n points.
(a) Is there a hypersurface in the orthant $\mathbb{R}^n_+$ going through these n ...

**5**

votes

**2**answers

409 views

### Maximize the intersection of a n-dimensional sphere and an ellipsoid.

I have the conjecture that the volume of the intersection between an $n$-dim sphere (of radius $r$) and an ellipsoid (with one semi-axis larger than $r$) is maximized when the two are concentric, but ...

**2**

votes

**2**answers

522 views

### Mean curvature of polyhedral surfaces

Whilst working on this problem, I've come across the work of Konrad Polthier on generalizing the notion of curature to discrete surfaces; much of his work is covered in his thesis, "Polyhedral ...

**20**

votes

**2**answers

1k views

### Functions whose gradient-descent paths are geodesics

Let $f(x,y)$ define a surface $S$
in $\mathbb{R}^3$ with a unique local minimum at $b \in S$.
Suppose gradient descent from any start point $a \in S$
follows a geodesic on $S$ from $a$ to $b$.
(Q1.)
...

**9**

votes

**2**answers

2k views

### An optimization problem for points on the sphere (master's dissertation)

First, by means of a disclaimer, some background. I am entering the fourth and final year of an undergraduate master's degree in maths, and a quarter of the maximum credit for this year will be for a ...

**21**

votes

**2**answers

1k views

### What is the best way to peel fruit?

A mango made me wonder about this. (See also this question, which is in a similar spirit.)
Fix $L >0$ and a smooth body (possibly nonconvexâ€”pears or bananas are fair game!) $B \subset ...