Ultrathin AlN/GaN crystalline porous freestanding nanomembranes are fabricated on Si(111) by selective silicon etching, and self-assembled into various geometries such as tubes, spirals, and curved sheets. Nanopores with sizes from several to tens of nanometers are produced in nanomembranes of 20-35 nm nominal thickness, caused by the island growth of AlN on Si(111). No crystal-orientation dependence is observed while releasing the AlN/GaN nanomembranes from the Si substrate indicating that the driving stress mainly originates from the zipping effect among islands during growth. Competition between different relaxation mechanisms is experimentally revealed for different nanomembrane geometries and well-described by numerical calculations. The cathodoluminescence emission from GaN nanomembranes reveals a weak peak close to the GaN bandgap, which is dramatically enhanced by electron irradiation.