Beltrami equation for the harmonic diffeomorphisms between surfaces
نویسندگان
چکیده
We study harmonic maps between surfaces, that are solutions to a nonlinear elliptic PDE. In Refs. Minsky (1992); Wolf (1989) it was proved diffeomorphisms, with nonvanishing Hopf differential, satisfy Beltrami equation of certain type: the imaginary part logarithm coefficient coincides differential. Therefore, is function. The real satisfies an differential equation, which in case constant curvature sinh-Gordon equation. this paper we also prove converse: if function, then target surface can be equipped metric, conformal original one, and solution map. solving equivalent map problem. Harmonic therefore classified by classification general problem still open. Different well-known hyperbolic plane related one-soliton Moreover, example proposed does not belong Solutions calculated for unified way, positive, negative zero surface.
منابع مشابه
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ژورنال
عنوان ژورنال: Nonlinear Analysis-theory Methods & Applications
سال: 2022
ISSN: ['1873-5215', '0362-546X']
DOI: https://doi.org/10.1016/j.na.2021.112546