Refined asymptotics for minimal graphs in the hyperbolic space

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Abstract

We study the boundary behaviors of solutions f to the Dirichlet problem for minimal graphs in the hyperbolic space with singular asymptotic boundaries and characterize the boundary behaviors of f at the points strictly located in the tangent cones at the singular points on the boundary. For n = 2, we also obtain a refined estimate of f.

Keywords

asymptotic behaviors minimal graphs singular domains 

MSC(2010)

35J70 35J93 
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Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11571019).

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Beijing International Center for Mathematical ResearchPeking UniversityBeijingChina
  2. 2.School of Mathematical SciencesPeking UniversityBeijingChina

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