We investigate p-harmonic maps, p ≥ 2, from a complete non-compact manifold into a non-positively curved target. First, we establish a uniqueness result for the p-harmonic representative in the homotopy class of a constant map. Next, we derive a Caccioppoli inequality for the energy density of a p-harmonic map and we prove a companion Liouville type theorem, provided the domain manifold supports a Sobolev-Poincaré inequality. Finally, we obtain energy estimates for a p-harmonic map converging, with a certain speed, to a given point.

Constancy of p-harmonic maps of finite q-energy into non-positively curved manifolds / S. Pigola, M. Rigoli, A. Setti. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 258:2(2008 Feb), pp. 347-362. [10.1007/s00209-007-0175-7]

Constancy of p-harmonic maps of finite q-energy into non-positively curved manifolds

M. Rigoli
Secondo
;
2008

Abstract

We investigate p-harmonic maps, p ≥ 2, from a complete non-compact manifold into a non-positively curved target. First, we establish a uniqueness result for the p-harmonic representative in the homotopy class of a constant map. Next, we derive a Caccioppoli inequality for the energy density of a p-harmonic map and we prove a companion Liouville type theorem, provided the domain manifold supports a Sobolev-Poincaré inequality. Finally, we obtain energy estimates for a p-harmonic map converging, with a certain speed, to a given point.
Energy estimates; P-Harmonic maps; Uniqueness and Liouville theorems
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/37506
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