Compactness of harmonic maps of surfaces with regular nodes
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866911906527182848 |
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| author | Park, Woongbae |
| author_facet | Park, Woongbae |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2012_14040 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Compactness of harmonic maps of surfaces with regular nodes Park, Woongbae Differential Geometry Algebraic Geometry Analysis of PDEs 58E20, 32G15 (Primary) 53C43, 14H15 (Secondary) 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. |
| title | Compactness of harmonic maps of surfaces with regular nodes |
| topic | Differential Geometry Algebraic Geometry Analysis of PDEs 58E20, 32G15 (Primary) 53C43, 14H15 (Secondary) |
| url | https://arxiv.org/abs/2012.14040 |