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Minimal graphs in the hyperbolic space with singular asymptotic boundaries

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Abstract

We study asymptotic behaviors of solutions f to the Dirichlet problem for minimal graphs in the hyperbolic space with singular asymptotic boundaries under the assumption that the boundaries are piecewise regular with positive curvatures, a case which also arises in the study of a Chaplygin gas. We derive an estimate of such solutions by the corresponding solutions in the intersections of interior tangent balls. The positivity of curvatures plays an important role.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Qing Han

  2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Weiming Shen & Yue Wang

Authors
  1. Qing Han
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  2. Weiming Shen
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  3. Yue Wang
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Corresponding author

Correspondence to Yue Wang.

Additional information

Communicated by A. Malchiodi.

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The first author acknowledges the support of NSF Grant DMS-1404596. The second author and the third author acknowledge the support of NSFC Grant 11571019.

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Han, Q., Shen, W. & Wang, Y. Minimal graphs in the hyperbolic space with singular asymptotic boundaries. Calc. Var. 58, 192 (2019). https://doi.org/10.1007/s00526-019-1655-4

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  • DOI: https://doi.org/10.1007/s00526-019-1655-4

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