Yamabe metrics on conical manifolds

Fuente: arXiv
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Main Authors: Freguglia, Mattia, Malchiodi, Andrea
Format: Preprint
Published: 2024
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author Freguglia, Mattia
Malchiodi, Andrea
author_facet Freguglia, Mattia
Malchiodi, Andrea
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2402_05927
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Yamabe metrics on conical manifolds
Freguglia, Mattia
Malchiodi, Andrea
Differential Geometry
Analysis of PDEs
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.
title Yamabe metrics on conical manifolds
topic Differential Geometry
Analysis of PDEs
url https://arxiv.org/abs/2402.05927