  We investigate reversible diffusion-influenced reactions of an isolated pair
in two dimensions. To this end, we employ convolution relations that permit
deriving the survival probability of the reversible reaction directly in terms
of the survival probability of the irreversible reaction. Furthermore, we make
use of the mean reaction time approximation to write the irreversible survival
probability in restricted spaces as a single exponential. In this way, we
obtain exact and approximative expressions in the time domain for the
reversible survival probability for three different two dimensional diffusion
spaces: The infinite and restricted plane as well as the surface of a sphere.
Our obtained results should prove useful in the context of membrane-bound
reversible diffusion-influenced reactions in cell biology.
