Garcia-Fernandez, M and Pritham Pingali, V and Yao, C (2021) Gravitating vortices with positive curvature. In: Advances in Mathematics, 388 .
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Abstract
We give a complete solution to the existence problem for gravitating vortices with non-negative topological constant c⩾0. Our first main result builds on previous results by Yang and establishes the existence of solutions to the Einstein-Bogomol'nyi equations, corresponding to c=0, in all admissible Kähler classes. Our second main result completely solves the existence problem for c>0. Both results are proved by the continuity method and require that a GIT stability condition for an effective divisor on the Riemann sphere is satisfied. For the former, the continuity path starts from a given solution with c=0 and deforms the Kähler class. For the latter result we start from the established solution in any fixed admissible Kähler class and deform the coupling constant α towards 0. A salient feature of our argument is a new bound Sg⩾c for the curvature of gravitating vortices, which we apply to construct a limiting solution along the path via Cheeger-Gromov theory. © 2021 Elsevier Inc.
| Item Type: | Journal Article |
|---|---|
| Publication: | Advances in Mathematics |
| Publisher: | Academic Press Inc. |
| Additional Information: | The copyright for this article belongs to Authors |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 07 Oct 2021 15:54 |
| Last Modified: | 07 Oct 2021 15:54 |
| URI: | http://eprints.iisc.ac.in/id/eprint/69649 |
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