极小图函数与 $p$-调和函数的存在性和非存在性
微分几何
2023-04-03 v3
摘要
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 with only one end if has asymptotically non-negative sectional curvature. On the other hand, we prove the existence of bounded non-constant minimal graphic and -harmonic functions on rotationally symmetric Cartan-Hadamard manifolds under optimal assumptions on the sectional curvatures.
引用
@article{arxiv.1701.00953,
title = {Existence and non-existence of minimal graphic and $p$-harmonic functions},
author = {Jean-Baptiste Casteras and Esko Heinonen and Ilkka Holopainen},
journal= {arXiv preprint arXiv:1701.00953},
year = {2023}
}
备注
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