
```
I want to visualize Ricci flow solution on the following sphere 

```

Let $r> 0$ 


$L = \{ (x cos \theta, x sin \theta, x) | r < x < R \}$


$S$ : $(z-\sqrt{2} r)^2 + x^2 + y^2 = r^2$ 


$T$ : $ (z- \sqrt{2} R)^2 + x^2 + y^2 = R^2$ 


If $R$ is sufficiently large, then we have a two dimensional sphere $U$ enclosed by
 $L$, $S$, and $T$.


The Ricci flow solution on $U$ shrinks fastly around region covered by $S$, but 
 the region covered by $L$ remains unchanged, since the Gaussian curvature is 0. 


This confuses me. Where is wrong ? 


MOTIVATION : I want to know the Ricci flow on a orbifold $O$ which is smooth except 
 one point. In generally, is there a solution on $O$ ? 
 Around a singuler point, the curvature is very large so that Ricci flow solution on $O$ 
 shrinks to the singular point fastly. 


If we consider normalized Ricci flow on $O$, the solution goes to a "canonical"
 orbifold ? 


What I say is that if $O$ is a two sphere with exactly one point singularity, then 
 the solution goes to $lim\_{r \rightarrow 0} U$ 


Anything related with my opinion is welcome. 



Ricci flow on two dimensional sphere
Ricci flow is an intrinsic flow, so (unless you were to somehow recast it as an extrinsic flow) it doesn't make sense to talk about what happens to surfaces in $\mathbb{R}^3$ under Ricci flow.


