  The study of dwarf galaxies and their environments provides crucial testbeds
for predictions of cosmological models and insights on the structure formation
on small cosmological scales. In recent years, many problems on the scale of
groups of galaxies challenged the current standard model of cosmology. We aim
to increase the sample of known galaxies in the Leo-I group, containing the
M\,96 subgroup and the Leo Triplet. This galaxy aggregate is located at the
edge of the Local Volume at a mean distance of 10.7 Mpc. We employ image
enhancing techniques to search for low-surface brightness objects in publicly
available gr images taken by the Sloan Digital Sky Survey within 500 square
degrees around the Leo-I group. Once detected, we perform surface photometry
and compare their structural parameters to other known dwarf galaxies in the
nearby universe. We found 36 new dwarf galaxy candidates within the search
area. Their morphology and structural parameters resemble known dwarfs in other
groups. Among the candidates 5 to 6 galaxies are considered as ultra diffuse
galaxies candidates. If confirmed, they would be some of the closest examples
of this galaxy type. We assessed the luminosity function of the Leo-I group and
find it to be considerably rich in dwarf galaxies, with twice the number of
galaxies as the Local Group at a limiting magnitude of M_V=-10 and a steeper
faint-end slope.
