科研之友
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摘要
Given an unbounded domain Omega of a Hadamard manifold M, it makes sense to consider the problem of finding minimal graphs with prescribed continuous data on its cone topology boundary, i.e., on its ordinary boundary together with its asymptotic boundary. In this article it is proved that under the hypothesis that the sectional curvature of M is <= 1, this Dirichlet problem is solvable if Omega satisfies a certain convexity condition at infinity and if partial derivative Omega is mean convex. We also prove that mean convexity of partial derivative Omega is a necessary condition, extending to unbounded domains some results that are valid on bounded ones.
- 出版日期2016-3
