Sparad:
| Huvudupphovsman: | |
|---|---|
| Materialtyp: | Preprint |
| Publicerad: |
2020
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| Ämnen: | |
| Länkar: | https://arxiv.org/abs/2012.14040 |
| Taggar: |
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Innehållsförteckning:
- In this paper, we formulate and prove a general compactness theorem for harmonic maps using Deligne-Mumford moduli space and families of curves. The main theorem shows that given a sequence of harmonic maps over a sequence of complex curves, there is a family of curves and a subsequence such that both the domains and the maps converge off the set of "non-regular" nodes. This provides a sufficient condition for a neck having zero energy and zero length. As a corollary, the following known fact can be proved: If all domains are diffeomorphic to $S^2$, both energy identity and zero distance bubbling hold.