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arXiv · 2607.27441

The toric CR Yamabe problem

Eveline Legendre·Carlo Scarpa·Christina W. Tønnesen-Friedman
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Abstract

We study the equivariant CR Yamabe problem for a fixed-point-free torus action on a co-oriented compact contact manifold. Such examples arise naturally in the study of Sasakian manifolds with constant scalar curvature. In the toric case, we show that this problem is equivalent to a kind of boundary value problem for an elliptic PDE on a pair of functions defined on a convex, polyhedral domain. We provide examples of solutions and prove that many contact toric manifolds admit compatible CR structures with distinct signs of CR Yamabe invariants.

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Eveline Legendre, Carlo Scarpa, Christina W. Tønnesen-Friedman. 2026-07-29. The toric CR Yamabe problem. https://arxiv.org/abs/2607.27441

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