@ulfworsoe presented JuMP-dev a reformulation of the Geometric Cone using Power Cone.
The transformation we use currently uses the Rotated Second Order Cone.
As discussed at the end of the talk, even if adding a RSOC constraint has a smaller impact on performance than adding a Power cone, the number of constraints grows more rapidly for the reformulation with RSOC so for solver supporting Power Cones, the default bridge should be the one with Power Cones.