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I have a few related questions on Gaussian curvature (

*K*) of surfaces and simply connected regions:

- 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? - 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?