Electron-phonon interactions in the monocation of corannulene are studied by using the hybrid Hartree-Fock (HF)/density-functional-theory (DFT) method in the Gaussian 98 program package. The C-C stretching mode of 1498 cm(-1) most strongly couples to the e1 highest occupied molecular orbitals (HOMO) in corannulene. The total electron-phonon coupling constant for the monocation (l(HOMO)) of corannulene is estimated to be 0.165 eV. The l(HOMO) value for corannulene is much larger than those for coronene and acenes with similar numbers of carbon atoms. The delocalized electronic structures and the intermediate characteristics between the strong sigma-orbital interactions and weak pi-orbital interactions originating from a bowl-shaped C(5v) geometry are the main reason that the l(HOMO) value for corannulene is much larger than those for planar D(6h) symmetric pi-conjugated coronene and D(2h) symmetric pi-conjugated acenes with similar numbers of carbon atoms. The electron transfer in the positively charged corannulene is also discussed. Intramolecular electron mobility (sigma(intra,monocation)) in the positively charged corannulene is estimated to be smaller than those for the positively charged pi-conjugated acenes and coronene. The reorganization energy for the positively charged corannulene (0.060 eV) is estimated to be larger than those for the positively charged acenes and coronene. The strong orbital interactions between two neighboring carbon atoms in the HOMO of corannulene with the bowl-shaped structure are the main reasons for the calculated results. Thus, the larger overlap integral between two neighboring molecules is needed for the positively charged corannulene to become a better conductor than those for positively charged coronene and acenes. The smaller density of states at the Fermi level n(0) values are enough for the conditions of the attractive electron-electron interactions to be realized in the monocation of corannulene than in the monocations of coronene and acenes with similar numbers of carbon atoms. The multimode problem is also treated in order to investigate how consideration of the multimode problem is closely related to the characteristics of the electron-phonon interactions.