Apparatus is provided including a prosthesis for implantation at a native semilunar valve of a native valve complex of a subject, the native valve complex having semilunar sinuses, the prosthesis including a valve prosthesis support, which includes a support structure including at least two engagement arms. Upon implantation of the prosthesis, each of the engagement arms is at least partially disposed within a respective one of the semilunar sinuses. A shape of at least one of the engagement arms is generally characterized by a function z″(r)>；=0, where z is a height of any given point on the at least one engagement arm measured along a longitudinal axis of the prosthesis, and r is a distance from the longitudinal axis to the given point. Other embodiments are also described.
