  The notion of maximal-spacing in several dimensions was introduced and
studied by Deheuvels (1983) for data uniformly distributed on the unit cube.
Later on, Janson (1987) extended the results to data uniformly distributed on
any bounded set, and obtained a very fine result, namely, he derived the
asymptotic distribution of different maximal-spacings notions. These results
have been very useful in many statistical applications. We extend Janson's
results to the case where the data are generated from a H\"older continuous
density that is bounded from below and whose support is bounded. As an
application, we develop a convexity test for the support of a distribution.
