Energy identity for the maps from a surface with tension field bounded in L p
Abstract
Let
M
be a closed Riemannian surface and
u
n
a sequence of maps from
M
to Riemannian manifold
N
satisfying
sup
n
(∥∇
u
n
∥
L
2
(M)
+∥τ(
u
n
)
∥
L
p
(M)
)≤Λ
for some
p>1
, where
τ(
u
n
)
is the tension field of the mapping
u
n
.
For the general target manifold
N
, if
p≥
6
5
, we prove the energy identity and neckless during blowing up.