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In this paper, the Hawking-Page phase transitions between the black holes andthermal anti-de Sitter (AdS) space are studied with the Gauss-Bonnet term inthe extended phase space, in which the varying cosmological constant plays therole of an effective thermodynamic pressure. The Gauss-Bonnet term exhibits itseffects via introducing the corrections to the black hole entropy and Gibbsfree energy. The global phase structures, especially the phase transitiontemperature $T_{\rm HP}$ and the Gibbs free energy $G$, are systematicallyinvestigated, first for the Schwarzschild-AdS black holes and then for thecharged and rotating AdS black holes in the grand canonical ensembles, withboth analytical and numerical methods. It is found that there are terminalpoints in the coexistence lines, and $T_{\rm HP}$ decreases at large electricpotentials and angular velocities and also decreases with the Gauss-Bonnetcoupling constant $\alpha$.

The Hawking-Page phase transitions in the extended phase space in the Gauss-Bonnet gravity