On p-harmonic maps and convex functions

Details On p-harmonic maps and convex functions On p-harmonic maps and convex functions

2009-04-29

arxiv.org/abs/0904.4497v2

Manuscripta Mathematica 131 (2010), no. 3-4, 537 - 546

Mathematics

Analysis of PDEs

8 pages

Scientific paper

10.1007/s00229-010-0335-7

We prove that, in general, given a $p$-harmonic map $F:M\to N$ and a convex function $H:N\to\mathbb{R}$, the composition $H\circ F$ is not $p$-subharmonic. 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.

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