Time periodic traveling curved fronts of bistable reaction–diffusion equations in RNRN

This paper is concerned with time periodic traveling curved fronts of bistable reaction–diffusion equations in RNRN with N≥3N≥3. For any given (N−2)(N−2)-dimensional smooth surfaces with the boundaries being compact sets in RN−1RN−1, we prove that there exists a cylindrically nonsymmetric traveling curved front under the assumption that all principal curvatures are positive everywhere.