An analytic proof of the stable reduction theorem

The stable reduction theorem says that a family of curves of genus g≥ 2 g ≥ 2 over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new this result for curves defined over C C , using the Kähler–Einstein metrics on the fibers to obtain the limiting stable curves at the punctures.