Curing mold for manufacturing a turbomachine component made of a composite material, starting from a preform made by laying up prepregs comprising reinforcing fibers impregnated in a thermosetting resin, the preform having a portion to be molded and at least one additional portion extending into the prolongation of the portion to be molded and forming an edge of the preform, the curing mold comprising: - a first body and a second body designed to be fitted together, the first and second bodies (11, 12) each comprising an internal surface (13, 14) itself comprising a peripheral area (15, 16) at which the first and second bodies (11, 12) are in contact with each other and a central area (17, 18) defining a fixed air gap between the first and second bodies (11, 12), the air gap being intended to accommodate the preform and itself comprising: ∘ a molding part with a shape complementary to the component to be manufactured, the molding part being intended to accommodate the portion to be molded of the preform, and ∘ at least one additional part located in a peripheral space of the air gap, the or each additional part being intended to accommodate an additional portion of the preform; - a heating member designed to heat the preform in the air gap to a first temperature, so as to reduce the viscosity of the resin; - at least one inflatable bladder housed in the central area (17, 18) of the internal surface (13, 14) of the first or second body (12, 13), facing an additional part of the air gap; - an injection member designed to inject fluid under pressure inside the bladder(s), so as to inflate the bladder(s) from a deflated state to an inflated state, and the or each bladder also being designed so that, in the inflated state, it compresses the additional portion of the preform located in the additional part of the air gap facing said bladder, so as to flush the resin from the additional portion of the preform towards the portion to be molded of the preform and thus put the preform under hydrostatic pressure, when the preform is located in the air gap and the heating member heats the preform to the first temperature. - a first body and a second body designed to be fitted together, the first and second bodies (11, 12) each comprising an internal surface (13, 14) itself comprising a peripheral area (15, 16) at which the first and second bodies (11, 12) are in contact with each other and a central area (17, 18) defining a fixed air gap between the first and second bodies (11, 12), the air gap being intended to accommodate the preform and itself comprising: ∘ a molding part with a shape complementary to the component to be manufactured, the molding part being intended to accommodate the portion to be molded of the preform, and ∘ at least one additional part located in a peripheral space of the air gap, the or each additional part being intended to accommodate an additional portion of the preform; ∘ a molding part with a shape complementary to the component to be manufactured, the molding part being intended to accommodate the portion to be molded of the preform, and ∘ at least one additional part located in a peripheral space of the air gap, the or each additional part being intended to accommodate an additional portion of the preform; - a heating member designed to heat the preform in the air gap to a first temperature, so as to reduce the viscosity of the resin; - at least one inflatable bladder housed in the central area (17, 18) of the internal surface (13, 14) of the first or second body (12, 13), facing an additional part of the air gap; - an injection member designed to inject fluid under pressure inside the bladder(s), so as to inflate the bladder(s) from a deflated state to an inflated state, and the or each bladder also being designed so that, in the inflated state, it compresses the additional portion of the preform located in the additional part of the air gap facing said bladder, so as to flush the resin from the additional portion of the preform towards the portion to be molded of the preform and thus put the preform under hydrostatic pressure, when the preform is located in the air gap and the heating member heats the preform to the first temperature.