Harmonic functions on minimal submanifold with cylindrical cone

In this paper, we study the relationship between the dimension of linear space of harmonic function with growth bounded by a fixed-degree polynomial on a minimal submanifold in Euclidean space and that on its one cylindrical tangent cone at infinity by using the method in [6, 7]. Specifically, if this degree does not coincide with any growth of polynomial-growth harmonic functions on the cone, then the corresponding dimensions are equal.