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Summary form only given, as follows. Atomic cavities provide a convenient way to store atoms without perturbing them too much. We have recently built such a cavity for cesium atoms. A curved mirror was made for an evanescent wave, formed by internal reflection of a quasiresonant laser beam at a curved glass surface. A cold cloud of cesium atoms was dropped onto the mirror (Fig. 1a) and observed to rebound up to 10 times (Fig. 1b). The mirror size and reflectivity were studied, and reasonable agreement with a simple theory was obtained. With 800 mW of laser power and a mirror of 1 mm diameter, we observed up to 73% of the atoms returning after each bounce. We will present these experimental results, and we will also discuss some prospects to investigate the quantum nature of the atomic motion in such a cavity.