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A new approach to some nonlinear geometric equations in dimension two

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Abstract

We give new arguments for several Liouville type results related to the equation −Δ u = Ke2u. The new approach is based on the holomorphic function associated with any solution, which plays a similar role as the Hopf differential for harmonic maps from a surface.

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824

    Fengbo Hang & Xiaodong Wang

Authors
  1. Fengbo Hang
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  2. Xiaodong Wang
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Correspondence to Fengbo Hang.

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Hang, F., Wang, X. A new approach to some nonlinear geometric equations in dimension two. Calc. Var. 26, 119–135 (2006). https://doi.org/10.1007/s00526-005-0372-3

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  • DOI: https://doi.org/10.1007/s00526-005-0372-3

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