The Geometry of ( p, q )-Harmonic Maps

Yan Wang and Kaige Jiang ()
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Yan Wang: School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
Kaige Jiang: School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, China

Mathematics, 2025, vol. 13, issue 17, 1-33

Abstract: This paper studies ( p , q ) -harmonic maps by unified geometric analytic methods. First, we deduce variation formulas of the ( p , q ) -energy functional. Second, we analyze weakly conformal and horizontally conformal ( p , q ) -harmonic maps and prove Liouville results for ( p , q ) -harmonic maps under Hessian and asymptotic conditions on complete Riemannian manifolds. Finally, we define the ( p , q ) - S S U manifold and prove that non-constant stable ( p , q ) -harmonic maps do not exist.

Keywords: ( p , q )-harmonic maps; variation formulas; Liouville results; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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