  We consider a monopoly seller who optimally auctions a single object to a
single potential buyer, with a known distribution of valuations. We show that a
tight lower bound on the seller's expected revenue is $1/e$ times the geometric
expectation of the buyer's valuation, and that this bound is uniquely achieved
for the equal revenue distribution. We show also that when the valuation's
expectation and geometric expectation are close, then the seller's expected
revenue is close to the expected valuation.
