manuscripta mathematica

, Volume 131, Issue 3–4, pp 537–546

On p-harmonic maps and convex functions

Article

Abstract

We prove that, in general, given a p-harmonic map F : MN and a convex function \({H : N \rightarrow \mathbb{R}}\), the composition \({H\circ F}\) is not p-subharmonic, if p ≠ 2. This answers in the negative an open question arisen from a paper by Lin and Wei. By assuming some rotational symmetry on manifolds and functions, we reduce the problem to an ordinary differential inequality. The key of the proof is an asymptotic estimate for the p-harmonic map under suitable assumptions on the manifolds.

Mathematics Subject Classification (2000)

Primary 58E20 Secondary 53C43 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly

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