{"title":"具有点质量的Monge-Ampère方程解的奇异结构","authors":"Connor Mooney, Arghya Rakshit","doi":"10.3934/mine.2023083","DOIUrl":null,"url":null,"abstract":"We construct new examples of Monge-Ampère metrics with polyhedral singular structures, motivated by problems related to the optimal transport of point masses and to mirror symmetry. We also analyze the stability of the singular structures under small perturbations of the data given in the problem under consideration.","PeriodicalId":54213,"journal":{"name":"Mathematics in Engineering","volume":" ","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2022-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Singular structures in solutions to the Monge-Ampère equation with point masses\",\"authors\":\"Connor Mooney, Arghya Rakshit\",\"doi\":\"10.3934/mine.2023083\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct new examples of Monge-Ampère metrics with polyhedral singular structures, motivated by problems related to the optimal transport of point masses and to mirror symmetry. We also analyze the stability of the singular structures under small perturbations of the data given in the problem under consideration.\",\"PeriodicalId\":54213,\"journal\":{\"name\":\"Mathematics in Engineering\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2022-04-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics in Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.3934/mine.2023083\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics in Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.3934/mine.2023083","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Singular structures in solutions to the Monge-Ampère equation with point masses
We construct new examples of Monge-Ampère metrics with polyhedral singular structures, motivated by problems related to the optimal transport of point masses and to mirror symmetry. We also analyze the stability of the singular structures under small perturbations of the data given in the problem under consideration.
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