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arXiv · 2510.17669

A Lichnerowicz equation in the Einstein-scalar field theory on non-CMC closed manifolds

Bartosz Bieganowski·Pietro d'Avenia·Jacopo Schino·Daniel Strzelecki
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Abstract

In the paper, we prove the existence of a positive and essentially bounded solution to a Lichnerowicz equation in the Einstein-scalar field theory on a closed manifold with non-constant mean curvature. In particular, the non-constant mean curvature gives rise to supercritical terms in the equation, on top of singular ones. We employ a recent fixed-point argument, which involves sub- and supersolutions. Additionally, we provide several conditions on the coefficients in the equation that prevent the existence of positive classical solutions.

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Bartosz Bieganowski, Pietro d'Avenia, Jacopo Schino, Daniel Strzelecki. 2025-10-20. A Lichnerowicz equation in the Einstein-scalar field theory on non-CMC closed manifolds. https://arxiv.org/abs/2510.17669

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