Compactness issues and bubbling phenomena for the prescribed Gaussian curvature equation on the torus

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• 作者：Luca Galimberti
• 关键词：53A30 ; 58E30
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：54
• 期：3
• 页码：2483-2501
• 全文大小：504 KB
• 参考文献：1.Borer, F., Galimberti, L., Struwe, M.: “Large-conformal metrics of prescribed Gauss curvature on surfaces of higher genus. Comment. Math. Helv. (2015)
  2.Ding, W.Y., Liu, J.: A note on the prescribing Gaussian curvature on surfaces. Trans. Am. Math. Soc. 347, 1059-066 (1995)
  3.Kazdan, J.L., Warner, F.W.: Curvature functions for compact \(2\) -manifolds. Ann. Math. 99(2), 14-7 (1974)
  4.Struwe, M.: Une estimation asymptotique pour le modèle de Ginzburg–Landau [An asymptotic estimate for the Ginzburg-Landau model]. C. R. Acad. Sci. Paris Sr. I Math. 317(7), 677-80 (1993)
  5.Zeidler, E.: Nonlinear Functional Analysis and its Applications III. Springer, New york (1985)
  
• 作者单位：Luca Galimberti (1)
  
  1. Departement Mathematik, ETH-Zürich, 8092, Zurich, Switzerland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Systems Theory and Control
  Calculus of Variations and Optimal Control
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0835

文摘

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). Mathematics Subject Classification 53A30 58E30