Conformal metrics of constant scalar curvature with unbounded volumes

Fuente: arXiv
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Main Authors: Gong, Liuwei, Li, Yanyan
Format: Preprint
Published: 2024
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author Gong, Liuwei
Li, Yanyan
author_facet Gong, Liuwei
Li, Yanyan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2406_06898
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Conformal metrics of constant scalar curvature with unbounded volumes
Gong, Liuwei
Li, Yanyan
Analysis of PDEs
Differential Geometry
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.
title Conformal metrics of constant scalar curvature with unbounded volumes
topic Analysis of PDEs
Differential Geometry
url https://arxiv.org/abs/2406.06898