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Energy identity of harmonic map flows from surfaces at finite singular time
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lin, Fanghua Wang, Changyou |
| Copyright Year | 1998 |
| Abstract | whereA is the 2nd fundamental form of N in RK (for simplicity we will omit g henceforth). Letu : M ×(0,∞) → N be a global weak solution to (1.1), which is smooth away from a finite number of singular points {(xi , ti )} ⊂ M ×(0,∞). The existence of such a u was obtained by Struwe [St], which was a natural extension of [SaU]. Let (x0,T0) be a singular point of u andB be a small neighborhood of x0, it is easy to show that, as t ↑ T0, u(·, t) → u(·,T0) in H 1 ∩C∞(B \ {x0},N ) locally, but not in H 1(B,N ). Moreover, nearx0, by suitably rescalingu(·, ti ) for ti ↑ T0, one can show there are finite many nonconstant harmonic maps ωi : S2 → N (1 ≤ i ≤ m), referred asbubbles, associated withu(·, ti ). It is clear that |
| Starting Page | 369 |
| Ending Page | 380 |
| Page Count | 12 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s005260050095 |
| Volume Number | 6 |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/s005260050095 |
| Alternate Webpage(s) | https://doi.org/10.1007/s005260050095 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
