Lesser auricular nerve
There is no such a nerve named "lesser auricular nerve". Therefore, the "Great auricular nerve" is incorrectly named "Greater auricular nerve".
The Great auricular nerve runs posteriorly to the ear, and is "greater," since it provides most of the innervation to the ear: the back of the ear, front of the ear and earlobe. The rest is provided by the auriculotemporal nerve, which supplies the skin anterior to the external auditory meatus.
