Yamabe metrics on conical manifolds

Abstract

We prove existence of Yamabe metrics on singular manifolds with conical points and conical links of Einstein type that include orbifold structures. We deal with metrics of generic type and derive a counterpart of Aubin's classical result. Interestingly, the singular nature of the metric determines a different condition on the dimension, compared to the regular case. We derive asymptotic expansions on the Yamabe quotient by adding a proper and implicit lower-order correction to standard bubbles, whose contribution to the expansion of the quotient can be determined combining the decomposition of symmetric two-tensor fields and Fourier analysis on the conical links.