Calculus of Variations and Geometric Measure Theory

M. Freguglia - A. Malchiodi

Yamabe metrics on conical manifolds

created by freguglia on 31 Jan 2024
modified on 22 Feb 2024


Submitted Paper

Inserted: 31 jan 2024
Last Updated: 22 feb 2024

Pages: 40
Year: 2024

ArXiv: 2402.05927 PDF


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.

Keywords: Conformal geometry, Singular Yamabe problem, Conical metrics