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We study the stochastic heat equation driven by an additive infinitedimensional fractional Brownian noise on the unit sphere $\mathbb{S}^{2}$. Theexistence and uniqueness of its solution in certain Sobolev space isinvestigated and sample path regularity properties are established. Inparticular, the exact uniform modulus of continuity of the solution intime/spatial variable is derived.

Regularity properties of the solution to a stochastic heat equation driven by a fractional Gaussian noise on ${\mathbb{S}}^2$