Coarse nodal counts on sub-Riemannian manifolds

Irene Silvestre-Roselló; Vukašin Stojisavljević

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arXiv · 2608.01446

Coarse nodal counts on sub-Riemannian manifolds

Irene Silvestre-Roselló·Vukašin Stojisavljević

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Abstract

We study coarse topology of nodal sets of linear combinations of eigenfunctions of sub-Laplacians. More precisely, we prove coarse versions of Courant's and B\'{e}zout's theorems for linear combinations of eigenfunctions of sub-Laplacians on compact nilmanifolds obtained as quotients of stratified groups. We conjecture the extensions of these results to general closed equiregular sub-Riemannian manifolds and outline a programme for proving them. The method we use combines topological persistence and anisotropic Sobolev theory of H\"{o}rmander vector fields, generalizing the ideas which have recently been implemented in the Riemannian case.

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Irene Silvestre-Roselló, Vukašin Stojisavljević. 2026-08-02. Coarse nodal counts on sub-Riemannian manifolds. https://arxiv.org/abs/2608.01446

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