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arXiv · 2606.22045

Dirichlet Energy of the Scalar Curvature

Ahmed Mohammed Cherif
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Abstract

In this article, we derive the first variation formula for the Dirichlet scalar curvature energy functional on Riemannian manifolds. Motivated by this variational framework, we introduce a natural generalization of Einstein metrics, called Dirichlet--Einstein metrics, and we investigate some of their fundamental properties.

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Ahmed Mohammed Cherif. 2026-06-20. Dirichlet Energy of the Scalar Curvature. https://arxiv.org/abs/2606.22045

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