Let
X
X
be a projective algebraic manifold, and
CH
k
(
X
,
1
)
\text {CH}^{k}(X,1)
the higher Chow group, with corresponding real regulator
r
k
,
1
⊗
R
:
CH
k
(
X
,
1
)
⊗
R
→
H
D
2
k
−
1
(
X
,
R
(
k
)
)
\text {r}_{k,1}\otimes {{\mathbb R}}: \text {CH}^k(X, 1)\otimes {{\mathbb R}} \to H_{\mathcal D}^{2k-1}(X,{{\mathbb R}}(k))
. If
X
X
is a general K3 surface or Abelian surface, and
k
=
2
k=2
, we prove the Hodge-
D
{\mathcal D}
-conjecture, i.e. the surjectivity of
r
2
,
1
⊗
R
\text {r}_{2,1}\otimes {{\mathbb R}}
. Since the Hodge-
D
{\mathcal D}
-conjecture is not true for general surfaces in
P
3
\mathbb {P}^{3}
of degree
≥
5
\geq 5
, the results in this paper provide an effective bound for when this conjecture is true.