Properties of infinite harmonic functions relative to Riemannian vector fields
AbstractWe employ Riemannian jets which are adapted to the Riemannian geometry to obtain the existence-uniqueness of inﬁnite harmonic functions in Riemannian spaces. We then show such functions are equivalent to those that enjoy comparison with Riemannian cones. Using comparison with cones, we show that the Riemannian distance is a supersolution to the inﬁnite Laplace equation, but is not necessarily a solution. We ﬁnd some geometric conditions under which the Riemannian distance is inﬁnite harmonic and under which it fails to be inﬁnite harmonic.
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