A Restriction for Singularities on Collapsing Orbifolds. (30th October 2011) - Ding, Yu
Abstract : Every pointp in an orbifoldX has a neighborhood that is homeomorphic toG p ∖ B r ( 0 ), whereG p is a finite group acting onB r ( 0 ) ⊂ ℝ n, so thatG p ( 0 ) = 0 . AssumeX is a Riemannian orbifold with isolated singularities that is collapsing, that is, X admits a sequence of metricsg i with uniformly bounded curvature, so that, for anyx ∈ X, the volume ofB 1 ( x ), with respect to the metricg i, goes to 0 asi → ∞ . For suchX, we prove that| G p | ≤ ( 2 π / 0.47 ) n ( n − 1 ) for all singularitiesp ∈ X .