{"title":"胶合空间和曲率下限","authors":"Christian Ketterer","doi":"arxiv-2408.13137","DOIUrl":null,"url":null,"abstract":"In this short note we survey theorems and provide conjectures on gluing\nconstructions under lower curvature bounds in smooth and non-smooth context.\nFocusing on synthetic lower Ricci curvature bounds we consider Riemannian\nmanifolds, weighted Riemannian manifolds, Alexandrov spaces, collapsed and\nnon-collapsed $RCD$ spaces, and sub-Riemannian spaces.","PeriodicalId":501444,"journal":{"name":"arXiv - MATH - Metric Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Glued spaces and lower curvature bounds\",\"authors\":\"Christian Ketterer\",\"doi\":\"arxiv-2408.13137\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this short note we survey theorems and provide conjectures on gluing\\nconstructions under lower curvature bounds in smooth and non-smooth context.\\nFocusing on synthetic lower Ricci curvature bounds we consider Riemannian\\nmanifolds, weighted Riemannian manifolds, Alexandrov spaces, collapsed and\\nnon-collapsed $RCD$ spaces, and sub-Riemannian spaces.\",\"PeriodicalId\":501444,\"journal\":{\"name\":\"arXiv - MATH - Metric Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Metric Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.13137\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Metric Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.13137","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this short note we survey theorems and provide conjectures on gluing
constructions under lower curvature bounds in smooth and non-smooth context.
Focusing on synthetic lower Ricci curvature bounds we consider Riemannian
manifolds, weighted Riemannian manifolds, Alexandrov spaces, collapsed and
non-collapsed $RCD$ spaces, and sub-Riemannian spaces.
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