Abstract.
This paper considers the existence of a local minimizer of a conformally invariant functional defined on a space of maps of a closed Riemann surface into a compact Riemannian manifold \(N\). The functional is defined for a given tensor \(H\) on \(N\) of type (1,2) and we call its extremal an \(H\)-surface. In fact, we prove that there exists a local minimizer of the functional in a given homotopy class under certain conditions on \(N\), \(H\) and the minimum of the Dirichlet integral of maps of the homotopy class.
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Received January 21, 1994 / Received in revised form October 24, 1995 / Accepted March 15, 1996
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Toda, M. On the existence of H-surfaces into Riemannian manifolds . Calc Var 5, 55–83 (1997). https://doi.org/10.1007/s005260050059
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DOI: https://doi.org/10.1007/s005260050059