1Department of Mathematics, University of Oklahoma, Norman, Oklahoma, 73019-0315, USA. E-mail: wwei@ou.edu
2CRM & McGill University, Department of Mathematics and statistics, Montreal, QC H3A 2K6, Canada. E-mail: jli@math.mcgill.ca
3Department of Mathematics, University of Toledo, Toledo, Ohio, 43606, USA. E-mail: lwu7@utnet.utoledo.edu
*Research was partially supported by NSF Award No DMS-0508661, OU Presidential International Travel Fellowship, and OU Faculty Enrichment Grant.
In this paper we prove that a convex function on ℝn is a p-subharmonic function, for every p > 1, and a C2 convex function on a Riemannian manifold is a p-subharmonic function f, for every p > 1. We also prove that a C2 convex function which is a submersion on a Riemannian manifold is a p-subharmonic function, for every p ≥ 1. This result is sharp, and improves authors’ previous work for p ≥ 2.
p-subharmonic function, convex function, submersion
