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Local Gradient Estimate for -harmonic functions on Riemannian Manifolds
For positive -harmonic functions on Riemannian manifolds, we derive a
gradient estimate and Harnack inequality with constants depending only on the
lower bound of the Ricci curvature, the dimension , and the radius of
the ball on which the function is defined. Our approach is based on a careful
application of the Moser iteration technique and is different from Cheng-Yau's
method employed by Kostchwar and Ni, in which a gradient estimate for positive
-harmonic functions is derived under the assumption that the sectional
curvature is bounded from below.Comment: 10 page
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