  Self-trapping of an electron due to its interaction with bending fluctuations
in a flexible crystalline membrane is considered. Due to the dependence of the
electron energy on the corrugations of the membrane, the electron can create
around itself an anomalously flat (or anomalously corrugated, depending on the
sign of the interaction constant) region and be confined there. Using the
Feynman path integral approach, the autolocalization energy and the size of the
self-trapped state (flexuron) are estimated. It is shown that typically the
size of the flexuron is of the order of the wavelength of fluctuations at the
border between harmonic and anharmonic regimes. The flexuron states are
connected with the fluctuation tail of the electron density-of-states, the
asymptotic behavior of this tail being determined by the exponent of the
renormalized bending rigidity.
