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November 2017 Barycenter technique and the Riemann mapping problem of Cherrier–Escobar
Martin Mayer, Cheikh Birahim Ndiaye
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J. Differential Geom. 107(3): 519-560 (November 2017). DOI: 10.4310/jdg/1508551224


We solve in the affirmative the remaining cases of the Riemann mapping problem of Cherrier–Escobar [35][38] first raised by Cherrier [35] in 1984. Indeed, performing a suitable scheme of the barycenter technique of Bahri–Coron [14] via the Almaraz–Chen’s bubbles [3][34], we completely solve all the cases left open after the work of Chen [34]. Hence, combining our work with the ones of Almaraz [2], Chen [34], Cherrier [35], Escobar [38][40] and Marques [55][56], we have that every compact Riemannian manifold with boundary, of dimension greater or equal than three, and with finite Sobolev quotient, carries a conformal scalar flat metric with constant mean curvature on the boundary.


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Martin Mayer. Cheikh Birahim Ndiaye. "Barycenter technique and the Riemann mapping problem of Cherrier–Escobar." J. Differential Geom. 107 (3) 519 - 560, November 2017.


Received: 15 June 2015; Published: November 2017
First available in Project Euclid: 21 October 2017

zbMATH: 06846970
MathSciNet: MR3715348
Digital Object Identifier: 10.4310/jdg/1508551224

Rights: Copyright © 2017 Lehigh University

Vol.107 • No. 3 • November 2017
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