Recent content by finsly

I really apologize with all of you for the incompleteness of the provided hypothesis. Actually, the manifold M is simply connected as well as its boundary \partial M, and these restrictions seems to exclude the latter counterexample (if I'm not wrong). And (finally) these are all the hypothesis...

First of all, thank you for your reply. Next, you're right, I forgot an hypothesis that could be crucial: f(p)\to -\infty as p approaches the boundary \partial M. Could this do any difference? Maybe, (but I don't know if this makes any sense...) an idea could be to work with the extended...

I'm trying to give an answer to the following problem, I hope someone could come in help! Consider a smooth n-dimensional manifold M with smooth (nonempty) boundary \partial M, and suppose given a function f: M\setminus \partial M \to \mathbb{R} (which one can assume to be differentiable)...