Constancy of p-harmonic maps of finite q-energy into non-positively curved manifolds |
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Authors: | Stefano Pigola Marco Rigoli Alberto G. Setti |
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Affiliation: | (1) Dipartimento di Fisica e Matematica, Università dell’Insubria-Como, via Valleggio 11, 22100 Como, Italy;(2) Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 Milano, Italy |
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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. |
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Keywords: | Uniqueness and Liouville theorems p-Harmonic maps Energy estimates |
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