  In this study, we explore the potential of utilizing the four Minkowski
functionals, which can fully describe the morphological properties of the
large-scale structures, as a robust tool for investigating the modified
gravity, particularly on non-linear and quasi-linear scales. With the
assistance of the N-body simulation, we employ the Minkowski functionals to
probe the Hu-Sawicki f(R) gravity model. The focus is on understanding the
morphorlogical properties extracted by the Minkowski functionals and their
sensitivity to modified gravity. Our analysis involves a comprehensive
examination of the cosmic variance arising from finite simulation volumes. By
systematically varying smoothing scales and redshifts, we quantify the
information encoded in the Minkowski functionals measured from the dark-matter
density field. The goal is to assess the capacity of the Minkowksi functionals
to constrain the model and explore potential improvements through their
combination. Additionally, we investigate the impact of using biased tracers
such as dark matter halos and the halo occupation distribution galaxies on the
modified gravity signatures within the Minkowksi functionals of the LSS.
Furthermore, we evaluate the influence of the redshift space distortion on the
observed results. In summary, our study suggests that the Minkowski functionals
of the large-scale structures hold promise as a stringent tool for constraining
modified gravity and offer valuable insights into the morphological features of
the cosmic web.
