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Systolic inequalities and the Horowitz-Myers conjecture
[Submitted on 6 Jun 2024 (v1), last revised 11 Jun 2026 (this ve · 2026-06-15 · via math updates on arXiv.org

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Abstract:Let $n$ be an integer with $3 \leq n \leq 7$, let $M$ be a compact manifold of dimension $n$ with boundary $\partial M$, and let $g$ be a Riemannian metric on $M$ with scalar curvature at least $-n(n-1)$. Under a topological assumption on $M$, we establish an inequality relating the infimum of the boundary mean curvature to the systole of the boundary $\partial M$. As a consequence, we obtain a new positive energy theorem, with equality being attained by the Horowitz-Myers metrics.

Submission history

From: S Brendle [view email]
[v1] Thu, 6 Jun 2024 17:28:14 UTC (17 KB)
[v2] Mon, 15 Jul 2024 10:22:11 UTC (19 KB)
[v3] Mon, 11 Nov 2024 21:08:11 UTC (19 KB)
[v4] Thu, 11 Jun 2026 20:20:19 UTC (21 KB)