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. The singular nature of the metric determines a different condition on the dimension, compared to the regular case.vIn dimension four, we can also find solutions of min-max type in presence of Z_2-orbifold points. Some perspectives for other singular manifolds will be discussed. This is joint work with Mattia Freguglia and Francesco Malizia.

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