Submitted Paper

Inserted: 5 mar 2026
Last Updated: 28 sep 2026

Year: 2026

Abstract:

We show that if the Hessian of a $C^{1,1}$ function has uniformly positive determinant almost everywhere then its index is locally constant, as conjectured by Šverák in 1992. We deduce this result as a consequence of a more general theorem valid for quasiregular gradient mappings.