Abstract
In this note we discuss how several results characterizing the qualitative behavior of solutions to the nonlinear Poisson equation can be generalized to harmonic maps with potential between complete Riemannian manifolds. This includes gradient estimates, monotonicity formulas, and Liouville theorems under curvature and energy assumptions.
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Open access funding provided by Austrian Science Fund (FWF). The author gratefully acknowledges the support of the Austrian Science Fund (FWF) through the START-Project Y963-N35 of Michael Eichmair.
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Branding, V. Some remarks on energy inequalities for harmonic maps with potential. Arch. Math. 109, 151–165 (2017). https://doi.org/10.1007/s00013-017-1049-9
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DOI: https://doi.org/10.1007/s00013-017-1049-9