Let
science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002212361630297X&_mathId=si1.gif&_user=111111111&_pii=S002212361630297X&_rdoc=1&_issn=00221236&md5=590e4612ee3feea83c643954d273ca1d" title="Click to view the MathML source">un be a sequence of mappings from a closed Riemannian surface
M to a general Riemannian manifold
N . If
science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002212361630297X&_mathId=si1.gif&_user=111111111&_pii=S002212361630297X&_rdoc=1&_issn=00221236&md5=590e4612ee3feea83c643954d273ca1d" title="Click to view the MathML source">un satisfies
where
science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002212361630297X&_mathId=si3.gif&_user=111111111&_pii=S002212361630297X&_rdoc=1&_issn=00221236&md5=2d6e42294fe20bfc00dd3a010b98c7e2" title="Click to view the MathML source">τ(un) is the tension field of
science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002212361630297X&_mathId=si1.gif&_user=111111111&_pii=S002212361630297X&_rdoc=1&_issn=00221236&md5=590e4612ee3feea83c643954d273ca1d" title="Click to view the MathML source">un, then the so called energy identity and neckless property hold during blowing up. This result is sharp by
Parker's example, where the tension fields of the mappings from Riemannian surface are bounded in
science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002212361630297X&_mathId=si4.gif&_user=111111111&_pii=S002212361630297X&_rdoc=1&_issn=00221236&md5=e428ebf4778fcc92e3cbee8aa2f62a9e" title="Click to view the MathML source">L1(M) but the energy identity fails.