Antarctic ice shelves are losing mass at drastically different rates, primarily due to differing rates of oceanic heat supply to their bases. However, a generalized theory for the inflow of relatively warm water into ice shelf cavities is lacking. This study proposes such a theory based on a geostrophically constrained inflow, combined with a threshold bathymetric elevation, the Highest Unconnected isoBath (HUB), that obstructs warm water access to ice shelf grounding lines. This theory captures ~90% of the variance in melt rates across a suite of idealized process-oriented ocean/ice shelf simulations with quasi-randomized geometries. Applied to observations of ice shelf geometries and offshore hydrography, the theory captures ~80% of the variance in measured ice shelf melt rates. These findings provide a generalized theoretical framework for melt resulting from buoyancy-driven warm water access to geometrically complex Antarctic ice shelf cavities.