We explore the Minkowski functionals of weak lensing convergence map to distinguish between f ( R ) gravity and the general relativity ( GR ) .
The mock weak lensing convergence maps are constructed with a set of high-resolution simulations assuming different gravity models .
It is shown that the lensing MFs of f ( R ) gravity can be considerably different from that of GR because of the environmentally dependent enhancement of structure formation .
We also investigate the effect of lensing noise on our results , and find that it is likely to distinguish F5 , F6 and GR gravity models with a galaxy survey of \sim 3000 degree ^ { 2 } and with a background source number density of n _ { g } = 30 ~ { } { arcmin } ^ { -2 } , comparable to an upcoming survey dark energy survey ( DES ) .
We also find that the f ( R ) signal can be partially degenerate with the effect of changing cosmology , but combined use of other observations , such as the cosmic microwave background ( CMB ) data , can help break this degeneracy .