# ASYMPTOTIC BEHAVIOR OF A-HARMONIC FUNCTIONS AND p-EXTREMAL LENGTH

• Published : 2010.03.31
• 29 3

#### Abstract

We describe the asymptotic behavior of functions of the Royden p-algebra in terms of p-extremal length. We also prove that each bounded $\cal{A}$-harmonic function with finite energy on a complete Riemannian manifold is uniquely determined by the behavior of the function along p-almost every curve.

#### Keywords

$\cal{A}$-harmonic function;p-harmonic boundary;comparison principle;maximum principle;p-extremal length;p-almost every curve

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