We have completely determined the Fermi surface in KFe$_2$As$_2$ via de Haas-van Alphen (dHvA) measurements. Fundamental frequencies $epsilon$, $alpha$, $zeta$, and $beta$ are observed in KFe$_2$As$_2$. The first one is attributed to a hole cylinder near the X point of the Brillouin zone, while the others to hole cylinders at the $Gamma$ point. We also observe magnetic breakdown frequencies between $alpha$ and $zeta$ and suggest a plausible explanation for them. The experimental frequencies show deviations from frequencies predicted by band structure calculations. Large effective masses up to 19 $m_e$ for $B parallel c$ have been found, $m_e$ being the free electron mass. The carrier number and Sommerfeld coefficient of the specific heat are estimated to be 1.01 -- 1.03 holes per formula unit and 82 -- 94 mJmol$^{-1}$K$^{-2}$, respectively, which are consistent with the chemical stoichiometry and a direct measure of 93 mJmol$^{-1}$K$^{-2}$ [H. Fukazawa textit{et al}., J. Phys. Soc. Jpn. textbf{80SA}, SA118 (2011)]. The Sommerfeld coefficient is about 9 times enhanced over a band value, suggesting the importance of low-energy spin and/or orbital fluctuations, and places KFe$_2$As$_2$ among strongly correlated metals. We have also performed dHvA measurements on Ba$_{0.07}$K$_{0.93}$Fe$_2$As$_2$ and have observed the $alpha$ and $beta$ frequencies.
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