do someone have an idea, how to prove that :

For every polyhedral metric $(S,d)$ of curvature $\leq -1$, (S=surface), there exists a sequence of smooth metrics, converging uniformly to $(S,d)$.

And why the metric in the neigbourhood of any singularity will be of the shape $dr^2+f^2(r)d\phi^2$ with $f$ a suitable function.

Thnak you for any answer


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.