  The classical Arzela-Ascoli theorem is a compactness result for families of
functions depending on bounds on the derivatives of the functions, and is of
invaluable use in many fields of mathemathics. In this paper, inspired by a
result of Corlette, we prove an analogous compactness result for families of
immersed submanifolds which depends only on bounds on the derivatives of the
second fundamental forms of these submanifolds. We then show how the result of
Corlette may be obtained as an immediate corollary.
