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Minimal immersions of closed surfaces in hyperbolic 3-manifold. Tarantello, Gabriella


Motivated by the the work of K. Uhlenbeck, we discuss minimal immersions of closed surfaces of genus larger than 1 on hyperbolic 3-manifold. In this respect we establish multiple existence for the Gauss-Codazzi equations and describe the asymptotic behaviour of the solutions in terms of the prescribed conformal structure and holomorphic quadratic differential whose real part identifies the corresponding second fundamental form. Joint work with Z. Huang and M. Lucia

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