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math.FA2026
Existence of extremal functions in higher-order affine Sobolev inequalities
Tristan Bullion-Gauthier
In this article, we prove the existence of extremal functions in higher-order affine Sobolev inequalities. Proofs rely on concentration-compactness methods in spaces of integer or…
math.CA2026
Kakeya conjecture and High-Rank Lattice von Neumann algebras
Mikael de la Salle
If the non-commutative L p space of SLn(Z) has the completely bounded approximation property for some non-trivial value of p, then some form of the Kakeya conjecture holds in dimen…