Virasoro Algebra and Löwner-kufarev Equations
نویسنده
چکیده
Virasoro algebra possesses a representation in the tangent space to the space of normalized univalent functions defined in the unit disk and smooth on its boundary. We discuss connections between representations of the Virasoro algebra and the Löwner-Kufarev equations in partial and ordinary derivatives. Virasoro generators turn to be conservative quantites for the Löwner-Kufarev ODE, and the Löwner-Kufarev PDE becomes a transition from the natural affine basis of the coefficients of univalent functions to the basis given by Virasoro generators. Finally, we give Hamiltonian and Lagrangian formulations of motions within the coefficient body.
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