This paper proposes a geothermal-solar-wind renewable energy hub framework for community multi-energy supplies. In this framework, multi-energy complementarities of geothermal-solar-wind hybrid renewable energy are fully explored based on electrolytic thermo-electrochemical effects of geothermal-to-hydrogen (GTH), which is integrated with the multi-energy conversion and storage devices for multi-energy supplies. In order to exploit the inherent multi-energy operational dispatchability and flexibility of geothermal-solar-wind renewables, a multi-energy coupling matrix is formulated for the modeling of production, conversion, storage, and consumption of hub-internal electricity, hydrogen and heating energy. A multi-energy operation scheme is further developed to dispatch the energy flows of the coupling matrix for cost-effective accommodation of community renewables. Case studies on a community microgrid under grid-connected and grid-disconnected modes are performed to verify the effectiveness and superiority of the proposed methodology. Simulations results show that the solar-wind accommodation can be improved by at most 1.59% with a significantly lower system operating cost.