A heart valve prosthesis for implantation at a native valve region of a heart, the prosthesis comprising: a valve support having an upstream portion and a downstream portion, the valve support configured to retain a prosthetic valve component therein; a plurality of support arms extending radially outward from the valve support and extending from the downstream portion of the valve support, each support arm being configured to extend from the downstream portion toward the upstream portion when the heart valve prosthesis is in an expanded configuration, and wherein in the expanded configuration each of the plurality of support arms has a curvilinear shape with a first curved region having a first radius of curvature, a second curved region having a second radius of curvature and an elongate region extending between the first curved region and the second curved region, with the first curved region being formed to curve toward the valve support proximate the downstream portion, the elongate region being formed to slant toward the valve support while joining the first curved region and the second curved region, and the second curved region being formed to curve away from the valve support proximate the upstream portion; and a radially-extending segment coupled to the upstream portion of the valve support, wherein when the heart valve prosthesis is in the expanded configuration the radially-extending segment is configured to engage a supra-annular surface of the native valve region, wherein in the expanded configuration atraumatic contact areas of the second curved regions of the plurality of support arms are configured to oppose the radially-extending segment such that a compressive force is exerted on an annulus at the native valve region by the atraumatic contact areas and the radially-extending segment so as to inhibit movement of the heart valve prosthesis. a valve support having an upstream portion and a downstream portion, the valve support configured to retain a prosthetic valve component therein; a plurality of support arms extending radially outward from the valve support and extending from the downstream portion of the valve support, each support arm being configured to extend from the downstream portion toward the upstream portion when the heart valve prosthesis is in an expanded configuration, and wherein in the expanded configuration each of the plurality of support arms has a curvilinear shape with a first curved region having a first radius of curvature, a second curved region having a second radius of curvature and an elongate region extending between the first curved region and the second curved region, with the first curved region being formed to curve toward the valve support proximate the downstream portion, the elongate region being formed to slant toward the valve support while joining the first curved region and the second curved region, and the second curved region being formed to curve away from the valve support proximate the upstream portion; and a first curved region having a first radius of curvature, a second curved region having a second radius of curvature and an elongate region extending between the first curved region and the second curved region, with the first curved region being formed to curve toward the valve support proximate the downstream portion, the elongate region being formed to slant toward the valve support while joining the first curved region and the second curved region, and the second curved region being formed to curve away from the valve support proximate the upstream portion; and a radially-extending segment coupled to the upstream portion of the valve support, wherein when the heart valve prosthesis is in the expanded configuration the radially-extending segment is configured to engage a supra-annular surface of the native valve region, wherein in the expanded configuration atraumatic contact areas of the second curved regions of the plurality of support arms are configured to oppose the radially-extending segment such that a compressive force is exerted on an annulus at the native valve region by the atraumatic contact areas and the radially-extending segment so as to inhibit movement of the heart valve prosthesis.