Calculus of Variations and Geometric Measure Theory

M. Mayer - C. B. Ndiaye

Barycenter technique and the Riemann mapping problem of Escobar

created by mayer1 on 23 Oct 2023
modified on 23 Jul 2026

[BibTeX]

Published Paper

Inserted: 23 oct 2023
Last Updated: 23 jul 2026

Year: 2015
Doi: https://doi.org/10.4310/jdg/1508551224

ArXiv: 1505.06198 PDF

Abstract:

We solve the remaining cases of the Riemann mapping problem of Escobar. Indeed, performing a suitable scheme of the barycenter technique of Bahri-Coron via the Chen's bubbles, we solve the cases left open after the work of Chen. Thus, combining our work with the ones of Almaraz, Chen, Escobar and Marques we have that every compact Riemannian manifold with boundary of dimension greater or equal than 3 carries a conformal scalar flat metric with constant mean curvature.