Constancy of the index for gradient mappings
Analysis of PDEs
2025-06-05 v1 Complex Variables
Differential Geometry
Abstract
We show that if the Hessian of a 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.
Cite
@article{arxiv.2506.03906,
title = {Constancy of the index for gradient mappings},
author = {André Guerra and Riccardo Tione},
journal= {arXiv preprint arXiv:2506.03906},
year = {2025}
}
Comments
16 pages