We study harmonic functions with polynomial growth on asymptotic cones of a nonnegatively Ricci curved manifold with Euclidean volume growth. Especially, we will give the classification of such harmonic functions.
Shouhei HONDA. "Harmonic functions on asymptotic cones with Euclidean volume growth." J. Math. Soc. Japan 67 (1) 69 - 126, January, 2015. https://doi.org/10.2969/jmsj/06710069