Gradient estimates for positive harmonic functions by stochastic analysis

Marc Arnaudon, Bruce K. Driver and Anton Thalmaier

Stochastic Processes and their Applications, 2007, vol. 117, issue 2, 202-220

Abstract: We prove Cheng-Yau type inequalities for positive harmonic functions on Riemannian manifolds by using methods of Stochastic Analysis. Rather than evaluating an exact Bismut formula for the differential of a harmonic function, our method relies on a Bismut type inequality which is derived by an elementary integration by parts argument from an underlying submartingale. It is the monotonicity inherited in this submartingale which allows us to establish the pointwise estimates.

Keywords: Harmonic; function; Curvature; Gradient; estimate; Harnack; inequality (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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