I Diverging Gaussian curvature and (non) simply connected regions

[Vini]

Hi there!
I have a few related questions on Gaussian curvature (K) of surfaces and simply connected regions:

1. Suppose that K approaches infinity in the neighborhood of a point (x1,x2) . Is there any relationship between the diverging points of K and (non) simply connected regions?
2. If K diverges in the neighborhood of a point (x1,x2), how may one prove that this point lies in a (non) simply connected region?

Thanks in advance.

 

[martinbn]

Hi there!
I have a few related questions on Gaussian curvature (K) of surfaces and simply connected regions:

1. Suppose that K approaches infinity in the neighborhood of a point (x1,x2) . Is there any relationship between the diverging points of K and (non) simply connected regions?
2. If K diverges in the neighborhood of a point (x1,x2), how may one prove that this point lies in a (non) simply connected region?

Thanks in advance.

I don't think so. It seems that the surface could have a cusp rather than a missing point.