  Geometric mean market makers (G3Ms), such as Uniswap and Balancer, represent
a widely used class of automated market makers (AMMs). These G3Ms are
characterized by the following rule: the reserves of the AMM must maintain the
same (weighted) geometric mean before and after each trade. This paper
investigates the effects of trading fees on liquidity providers' (LP)
profitability in a G3M, as well as the adverse selection faced by LPs due to
arbitrage activities involving a reference market. Our work expands the model
described in previous studies for G3Ms, integrating transaction fees and
continuous-time arbitrage into the analysis. Within this context, we analyze
G3M dynamics, characterized by stochastic storage processes, and calculate the
growth rate of LP wealth. In particular, our results align with and extend the
results concerning the constant product market maker, commonly referred to as
Uniswap v2.
