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arXiv · 2604.08738

A Conformally Invariant Dirac-type Equation on Compact Spin Manifolds: the Effect of the Geometry

Ali Maalaoui·Vittorio Martino
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Abstract

Given a closed Riemannian Spin manifold $(M,g)$ of dimension greater or equal than four, we consider a generalized conformally invariant equation involving the Dirac operator with a non-linearity of convolution type. We show that the Aubib-type inequality corresponding to the problem is always strict, unless $(M,g)$ is conformal to the round sphere. In particular, this result provides an existence result for a ground state to the conformal Dirac-Einstein problem in dimension four. We point out that aside from some perturbative or special cases, this presents the first general existence result for the conformal Dirac-Einstein equations in dimension four.

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Ali Maalaoui, Vittorio Martino. 2026-04-09. A Conformally Invariant Dirac-type Equation on Compact Spin Manifolds: the Effect of the Geometry. https://arxiv.org/abs/2604.08738

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