Troyanov, Marc2008-03-172008-03-172008-03-17199110.1016/S0294-1449(16)30255-4https://infoscience.epfl.ch/handle/20.500.14299/20141We study sequences of metrics on a compact surface with bounded area and curvature and I prove that if the conformalstructure of these metrics remains bounded, then either the sequence contains a convergent subsequence, or there exists a point at which a certain amount of positive curvature concentrates. The level of concentration is computed.text::journal::journal article::research article