On mean-convex Alexandrov embedded surfaces in the 3-sphere (Q495596)

The authors consider a class of complete immersed surfaces \(M\) in the unit round 3-sphere \(S^3\). It is assumed that these surfaces are mean-convex Alexandrov embedded. This condition means that the immersion \(M\to S^3\) can be extended to an immersion of a 3-dimensional manifold \(N\to S^3\) with boundary \(\partial N=M\). The authors determine under which conditions it is possible to deform continuously these preserving mean-convex Alexandrov embeddedness.