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Abstract On a complete p-nonparabolic 3-dimensional manifold with non-negative scalar curvature and vanishing second homology, we establish a sharp monotonicity formula for the proper p-Green function along its level sets for 1p3. This can be viewed as a generalization of the recent result by Munteanu-Wang 43 in the case of p=2. No smoothness assumption is made on the p-Green function when 1p 2. Several rigidity results are also proven.
Chan et al. (2024) studied this question.