Abstract
We study expansions near the boundary of solutions to the Dirichlet problem for the constant mean curvature equation in the hyperbolic space. With a characterization of remainders of the expansion by multiple integrals, we establish optimal asymptotic expansions of solutions with boundary values of finite regularity and demonstrate a slight loss of regularity for coefficients.
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The first author acknowledges the support of NSF Grant DMS-1404596. The second author acknowledges the support of NSF of China under Grant 12001383.
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Han, Q., Wang, Y. Boundary expansions for constant mean curvature surfaces in the hyperbolic space. Math. Z. 300, 851–879 (2022). https://doi.org/10.1007/s00209-021-02824-5
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DOI: https://doi.org/10.1007/s00209-021-02824-5