Täcklind uniqueness classes for heat equation on noncompact Riemannian manifolds

We describe uniqueness classes for solution of the Cauchy problem for the heat equation on a connected noncompact complete Riemannian manifold. For the case of manifolds with boundary, we assume that the solution satisfies the Dirichlet and Neumann conditions on the boundary.
Uniqueness classes are determined by a non-negative function growing no faster than the distance from a fixed point along a geodesics. The classes are similar to uniqueness classes of Täcklind type for the equation on the real line.