Abstract:Let $(M,g_0)$ be a closed Riemannian manifold of dimension $n \geq 25$ with positive Yamabe invariant $Y(M,g_0)>0$ and positive fourth-order invariant $Y_4(M,g_0)>0$. We show that, arbitrarily $C^1$-close to $g_0$, there exists a Riemannian metric such that, within its conformal class, one can find infinitely many smooth metrics with the same constant $Q$-curvature and arbitrarily large energy. Moreover, within this conformal class, there exists a sequence of smooth metrics with constant $Q$-curvature equal to $n(n^2-4)/8$ and unbounded volume. This extends to the $Q$-curvature setting the result previously obtained for the scalar curvature in Marques (2015) (see also Gond and Li (2025)). The proof is based on constructing small perturbations of multiple standard bubbles that are glued together.
From: Almir Silva Santos [view email]
[v1]
Mon, 15 Dec 2025 19:00:58 UTC (48 KB)
[v2]
Wed, 24 Jun 2026 16:06:51 UTC (48 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。