We study the growth of harmonic functions on complete Riemann-ian manifolds where the extrinsic diameter of geodesic spheres is sublinear. It is an generalization of a result of A. Kazue. We also get a Cheng and Yau estimates for the gradient of harmonic functions.
Local Gradient Estimate for $p$-harmonic functions on Riemannian Manifolds
Analysis of harmonic functions under lower bounds of $N$-weighted Ricci curvature with $\varepsilon$-range
Equivariant discretizations of diffusions and harmonic functions of bounded growth
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