Apparatus and methods are described including a valve frame defining a frame aperture and at least one arm attached to a portion of the valve frame on a ventricular side of said frame aperture. The at least one arm is configured to extend radially from the portion of the valve frame such that a chord receiving surface of the arm is sized and shaped to deploy among a region of the chords of the native mitral valve. The arm is curved, with an interior of the arm facing a direction in which the valve frame is configured to be rotated during deployment of the prosthetic mitral valve apparatus within the native mitral valve and with the arm having a concavely rounded leading edge facing at least partially in a circumferential direction. Other applications are also described.