We present mid-infrared photometry of three very young brown dwarfs located in the $rho$ Ophiuchi star-forming region -- GY5, GY11 and GY310 --obtained with the Subaru 8-meter telescope. All three sources were detected at 8.6 and 11.7$mu$m, confirming the presence of significant mid-infrared excess arising from optically thick dusty disks. The spectral energy distributions of both GY310 and GY11 exhibit strong evidence of flared disks; flat disks can be ruled out for these two brown dwarfs. The data for GY5 show large scatter, and are marginally consistent with both flared and flat configurations. Inner holes a few substellar radii in size are indicated in all three cases (and especially in GY11), in agreement with magnetospheric accretion models. Finally, our 9.7$mu$m flux for GY310 implies silicate emission from small grains on the disk surface (though the data do not completely preclude larger grains with no silicate feature). Our results demonstrate that disks around young substellar objects are analogous to those girdling classical T Tauri stars, and exhibit a similar range of disk geometries and dust properties.
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