Leave $ (R, mathfrak m, k) $ be a ring of local dimension of Gorenstein $ 2 $ such that $ mu ( mathfrak m ^ 2) (= dim_k mathfrak m ^ 2 / mathfrak m ^ 3) le 4 $ .

So it is true that $ R $ it is regular? Or at least it's true that $ R $ It has minimal multiplicity, that is $ e (R) = mu ( mathfrak m) -1 $ ?

here $ e (R) = d! lim_ {n to infty} dfrac {l (R / mathfrak m ^ n)} {n ^ d} $ , where $ d = dim R $ so in our case $ e (R) = 2 lim_ {n to infty} dfrac {l (R / mathfrak m ^ n)} {n ^ 2} $