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arXiv · 1911.02680

Uniformization Theorems: Between Yamabe and Paneitz

Cheikh Birahim Ndiaye·Yannick Sire·Liming Sun
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Abstract

This paper is devoted to several existence results for a generalized version of the Yamabe problem. First, we prove the remaining global cases for the range of powers $\gamma\in (0,1)$ for the generalized Yamabe problem introduced by Gonzalez and Qing. Second, building on a new approach by Case and Chang for this problem, we prove that this Yamabe problem is solvable in the Poincar\'{e}-Einstein case for $\gamma\in (1,\min\{2,n/2\})$ provided the associated fractional GJMS operator satisfies the strong maximum principle.

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Cheikh Birahim Ndiaye, Yannick Sire, Liming Sun. 2019-11-06. Uniformization Theorems: Between Yamabe and Paneitz. https://arxiv.org/abs/1911.02680

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