Diverging Gaussian curvature and (non) simply connected regions

In summary, the conversation discusses the relationship between Gaussian curvature (K) and simply connected regions. It is unclear if there is a relationship between the diverging points of K and (non) simply connected regions, and it may be difficult to prove that a point lies in a (non) simply connected region if K diverges in its neighborhood.
  • #1
3
1
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.
 
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  • #2
Vini said:
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.
 

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