@geocalc33 Hang on a bit.

@geocalc33 Ok now what's your question?

@user21820 My question is basically about creating a mathematical object only from knowing what it's projections are

Consider a cube prescribed with a family of real analytic functions on each face s.t. the shadow of the object inside the cube is cast precisely onto each face (light is shown from opposite faces) and maps directly onto the analytic functions. In some sense the functions encode the shape of the object (3-manifold) inside the cube. Is the 3-manifold necessarily unique, assuming you explicitly make a choice for the functions on the boundary?

Maybe this is a completely ridiculous question, but just wanted to ask

@geocalc33 I think you need to make your question more mathematically precise.

how?

let me know if you have any suggestions cause I'm stuck

"shadow" is not a mathematical notion. Nor are "cast" and "light".

Moreover, under any reasonable interpretation, it makes no sense to think that the projection of a 3-manifold projects is differentiable, not to say real-analytic!

ohh

I'm just starting from real analytic curves on the boundary and asking about a unique construction of the manifold with boundary

in other words it's my assumption

@geocalc33 And that's a different question!

And you still need to define all those non-mathematical terms, otherwise it's not a mathematical question.

so for example, the real analytic functions may be, $f(x)=x^n$ where $n \in \Bbb R_{>0}$

like that?

thanks that actually really helped :)

@geocalc33 No... I know what real-analytic functions are. But there is no mathematical definition of "shadow". You still have not defined it.

← 19 messages moved from Basic Mathematics