{"title":"Some results on the weighted Yamabe problem with or without boundary","authors":"Pak Tung Ho , Jinwoo Shin , Zetian Yan","doi":"10.1016/j.bulsci.2025.103658","DOIUrl":null,"url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>,</mo><mi>g</mi><mo>,</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>ϕ</mi></mrow></msup><mi>d</mi><msub><mrow><mi>V</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>,</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo><mi>ϕ</mi></mrow></msup><mi>d</mi><msub><mrow><mi>A</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>,</mo><mi>m</mi><mo>)</mo></math></span> be a compact smooth metric measure space with boundary with <span><math><mi>n</mi><mo>⩾</mo><mn>3</mn></math></span>. In this article, we consider several Yamabe-type problems on a compact smooth metric measure space with or without boundary: uniqueness problem on the weighted Yamabe problem with boundary, characterization of the weighted Yamabe solitons with boundary and the existence of positive minimizers in the weighted Escobar quotient.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"203 ","pages":"Article 103658"},"PeriodicalIF":1.3000,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin des Sciences Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0007449725000843","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Let be a compact smooth metric measure space with boundary with . In this article, we consider several Yamabe-type problems on a compact smooth metric measure space with or without boundary: uniqueness problem on the weighted Yamabe problem with boundary, characterization of the weighted Yamabe solitons with boundary and the existence of positive minimizers in the weighted Escobar quotient.