Existence and nonexistence 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 nonnegative sectional curvature. On the other hand, we prove the existence of bounded nonconstant minimal graphic and $p$harmonic functions on rotationally symmetric CartanHadamard manifolds under optimal assumptions on the sectional curvatures.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 DOI:
 10.48550/arXiv.1701.00953
 arXiv:
 arXiv:1701.00953
 Bibcode:
 2017arXiv170100953C
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 The authors are grateful to Professor Luciano Mari who pointed out an error in the proof of the previous version of Proposition 3.1 To appear in Proc. Roy. Soc. Edinburgh Sect. A