Abstract
In the spirit of the previous paper (Borer et al., Commun Math Helv, 2015), where we dealt with the case of a closed Riemann surface \((M,g_0)\) of genus greater than one, here we study the behaviour of the conformal metrics \(g_\lambda \) of prescribed Gauss curvature \(K_{g_\lambda } = f_0 + \lambda \) on the torus, when the parameter \(\lambda \) tends to one of the boundary points of the interval of existence of \(g_\lambda \), and we characterize their “bubbling behavior” as in Borer et al. (Commun Math Helv, 2015).
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References
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Acknowledgments
I would like to thank Michael Struwe for the guidance through the project which led to this paper.
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Communicated by A. Malchiodi.
Supported by SNF Grant 200021_140467/1.
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Galimberti, L. Compactness issues and bubbling phenomena for the prescribed Gaussian curvature equation on the torus. Calc. Var. 54, 2483–2501 (2015). https://doi.org/10.1007/s00526-015-0872-8
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DOI: https://doi.org/10.1007/s00526-015-0872-8