5
$\begingroup$

Let $X$ be a finite dimensional (possibly compact) Alexandrov space with curvature $\geq K$. Is it true that its boundary is again Alexandrov space with curvature bounded from below? If yes, is the curvature at least $K$?

$\endgroup$

1 Answer 1

5
$\begingroup$

This is an open problem.

It is a special case of the following question:

Is it true that every extremal subset is again an Alexandrov space?

The answer to this question is "No". Petrunin has constructed a counterexample in codimension three, here.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.