| Abstract: |
| Preliminary I will expose a technique developed with T. Rivi\`{e}re to prove energy identities for limits of sequences of solutions of conformally invariant problem in dimension $2$. I will explain in the following how with L. Lin and R. Petrides, we transpose it to open problems in the higher dimension or with free boundary and how it permits to prove the convexity of certain functional around their critical point of low energy. |
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