Let $X$ be a compact 2-dimensional Alexandrov space with curvature at least $\kappa$. My question is somewhat vague.
What is known about the boundary of $X$?
1) Is the boundary homeomorphic to a finite union of circles?
2) Is it possible to say that in certain generalized sense the boundary has non-negative second fundamental form (in other words, geodesic curvature)?
3) Assume that the diameter of $X$ is at most $D$. It is true that the number of connected components of the boundary is at most a constant depending on $\kappa, D$ only? Does the 1-dimensional Hausdorff measure of the boundary have such an upper bound?
Any other information and references will be helpful.