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The axial-vector form factors and axial-vector constants of the baryondecuplet are investigated within a pion mean-field approach, which is alsoknown as the chiral quark-soliton model. Given an axial-vector current with aspecified flavor, there are four different form factors of a decuplet baryon.When we consider the singlet, triplet, and octet axial-vector currents, we havetwelve different form factors for each member of the baryon decuplet. Wecompute all these axial-vector form factors of the baryon decuplet, taking intoaccount the rotational $1/N_c$ corrections and effects of flavor SU(3) symmetrybreaking. We find that, for a given flavor, two of the form factors for adecuplet baryon are only independent within the present approach. We firstexamine properties of the axial-vector form factors of the $\Delta^+$ isobarand $\Omega^-$ hyperon. We also compare the results of the triplet axial-vectorform factors of $\Delta^+$ with those from lattice QCD and those of the presentwork for the axial-vector constants of the baryon decuplet with the latticedata. All the results for other members of the baryon decuplet are thenpresented. The results of the axial charges are compared with those of otherworks. The axial masses and axial radii are also discussed.

Axial-vector form factors of the baryon decuplet with flavor SU(3) symmetry breaking