Existence and non-existence of minimal graphic and $p$-harmonic functions

Abstract : We prove that every entire solution of the minimal graph equation that is bounded from below and has at most linear growth must be constant on a complete Riemannian manifold $M$ with only one end if $M$ has asymptotically non-negative sectional curvature. On the other hand, we prove the existence of bounded non-constant minimal graphic and $p$-harmonic functions on rotationally symmetric Cartan-Hadamard manifolds under optimal assumptions on the sectional curvatures.
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https://hal.archives-ouvertes.fr/hal-01665512
Contributor : Jean-Baptiste Casteras <>
Submitted on : Saturday, December 16, 2017 - 7:31:19 AM
Last modification on : Tuesday, April 17, 2018 - 9:04:28 AM

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  • HAL Id : hal-01665512, version 1
  • ARXIV : 1701.00953

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Jean-Baptiste Casteras, Esko Heinonen, Ilkka Holopainen. Existence and non-existence of minimal graphic and $p$-harmonic functions. 2017. ⟨hal-01665512⟩

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