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Strongness conjecture for Sobolev metrics on the space of Sobolev surfaces
Strongness conjecture. Sobolev metrics of order $n\geq 3$ should be strong Riemannian metrics on $\mathcal I^n(M,\mathbb R^d)$ .
Conjectureopenriemannian-geometry sobolev-metrics spaces-of-surfacesarXiv posted 2 days ago

Strongness conjecture for Sobolev metrics on the space of Sobolev surfaces