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Seminar on Complex Analysis (Gonchar Seminar)
March 17, 2014 18:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)
 


Liouville equation on compact bordered surfaces

A. B. Bogatyrev

Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow

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Abstract: Poincare used the Liouville equation “exponent is half-Laplacian” to solve the problem of uniformization, i.e. restoration of a hyperbolic structure on a surface from its conformal structure. In the case of a bordered surface the equation must be supplemented by the boundary conditions. Different conditions lead to different hyperbolic metrics. Also we propose a conformally invariant action for the Liouville equation.

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