Seminar Analysis: Cheikh Ndiaye (Universität Tübingen)

Barycenter technique and two remaining questions in Geometric Analysis

In this talk, we will present our recent solutions of the remaining cases of the boundary Yamabe problem and the Riemann mapping problem asked by Escobarin 1992. Rather than discussing our arguments of proofs, we will focus more on explaining the barycenter technique of Bahri-Coron which we employ. We hope by doing this to allow an easier understanding for the audience, since it seems to us, that even among experts, the barycenter technique is not known like the minimizing technique of Aubin-Schoen. Moreover, we hope also the audience to see how naturally the barycenter technique fits into conformally invariant variational problems verifying the structure of quantization and strong interaction phenomena.

(Joint work with M. Mayer of University of Giessen)

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