Conformal metrics of constant scalar curvature with unbounded volumes

Liuwei Gong; Yanyan Li

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arXiv · 2406.06898

Conformal metrics of constant scalar curvature with unbounded volumes

Liuwei Gong·Yanyan Li

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Abstract

For $n\geq 25$, we construct a smooth metric $\tilde{g}$ on the standard $n$-dimensional sphere $\mathbb{S}^n$ such that there exists a sequence of smooth metrics $\{\tilde{g}_k\}_{k\in\mathbb{N}}$ conformal to $\tilde g$ where each $\tilde g_k$ has scalar curvature $R_{\tilde{g}_k}\equiv 1$ and their volumes $\text{Vol}(\mathbb{S}^n,\tilde{g}_k)$ tend to infinity as $k$ approaches infinity.

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Liuwei Gong, Yanyan Li. 2024-06-11. Conformal metrics of constant scalar curvature with unbounded volumes. https://arxiv.org/abs/2406.06898

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