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On Harmonic Close-To-Convex Functions
Computational Methods and Function Theory, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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p-Harmonic Maps and Convex Functions
Geometriae Dedicata, 1999The following theorem is proved. Let \(M\) be a complete noncompact Riemannian manifold, \(N\) a simply connected Riemannian manifold of nonpositive curvature, and \(\varphi:M\to N\) a \(C^1\) \(p\)-harmonic map. Then \(\varphi\) is constant, provided that \(\int_M\|d\varphi \|^{p-1}< \infty\).
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Completely Convex and Positive Harmonic Functions
SIAM Journal on Mathematical Analysis, 1975A completely convex function is a positive real-valued function on a real interval whose even derivatives alternate in sign. The author shows that every completely convex function is the restriction to the real line of a positive harmonic function in a vertical strip which is completely convex in x for each y.
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