期刊論文
| 學年 | 111 |
|---|---|
| 學期 | 2 |
| 出版（發表）日期 | 2023-04-28 |
| 作品名稱 | On the problem of prescribing weighted scalar curvature and the weighted Yamabe flow |
| 作品名稱（其他語言） | |
| 著者 | Pak Tung Ho, Jinwoo Shin |
| 單位 | |
| 出版者 | |
| 著錄名稱、卷期、頁數 | Analysis and Geometry in Metric Spaces 11(1), 20220152 |
| 摘要 | The weighted Yamabe problem introduced by Case is the generalization of the Gagliardo-Nirenberg inequalities to smooth metric measure spaces. More precisely, given a smooth metric measure space (M,g,e−ϕdVg,m) , the weighted Yamabe problem consists on finding another smooth metric measure space conformal to (M,g,e−ϕdVg,m) such that its weighted scalar curvature is equal to λ+μe−ϕ∕m for some constants μ and λ , satisfying a certain condition. In this article, we consider the problem of prescribing the weighted scalar curvature. We first prove some uniqueness and nonuniqueness results and then some existence result about prescribing the weighted scalar curvature. We also estimate the first nonzero eigenvalue of the weighted Laplacian of (M,g,e−ϕdVg,m) . On the other hand, we prove a version of the conformal Schwarz lemma on (M,g,e−ϕdVg,m) . All these results are achieved by using geometric flows related to the weighted Yamabe flow. We also prove the backward uniqueness of the weighted Yamabe flow. Finally, we consider weighted Yamabe solitons, which are the self-similar solutions of the weighted Yamabe flow. |
| 關鍵字 | Yamabe problem;Yamabe soliton;smooth metric measure space |
| 語言 | en |
| ISSN | 2299-3274 |
| 期刊性質 | 國外 |
| 收錄於 | SCI Scopus |
| 產學合作 | |
| 通訊作者 | Pak Tung Ho |
| 審稿制度 | 是 |
| 國別 | NLD |
| 公開徵稿 | |
| 出版型式 | ,電子版 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/124456 ) |