Constancy of the index for gradient mappings

André Guerra; Riccardo Tione

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arXiv · 2506.03906

Constancy of the index for gradient mappings

André Guerra·Riccardo Tione

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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 \v{S}ver\'ak in 1992. We deduce this result as a consequence of a more general theorem valid for quasiregular gradient mappings.

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André Guerra, Riccardo Tione. 2025-06-04. Constancy of the index for gradient mappings. https://arxiv.org/abs/2506.03906

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