Peking Univ, Dept Tech Phys, Beijing 100871, Peoples R China
; Peking Univ, MOE Lab Heavy Ion Phys, Beijing 100871, Peoples R China
; Natl Lab Heavy Ion Accelerator, Ctr Theoret Nucl Phys, Lanzhou 730000, Peoples R China
; Inst High Energy Phys, Beijing 100039, Peoples R China
; Pingdingshan TV Univ, Pingdingshan 467000, Peoples R China
; Peking Univ, Dept Phys, Beijing 100871, Peoples R China
Effects of neutrino trapping on K and (K) over bar production and (K) over bar condensation in supernova matter are studied in the density-dependent relativistic hadron field theory and in the nonlinear sigma-omega model with the parameter set Tm1. Our results show that critical densities for (K) over bar condensation with neutrino trapping are shifted to higher densities compared with those of neutrino free. Threshold energies for K and (K) over bar production are not sensitive to the effects induced by neutrino trapping. Meanwhile, it is shown that the effects of neutrino trapping decrease the maximum masses of protoneutron stars.