{"title":"三角曲线自交数的锐界","authors":"Sergei Kalmykov, Leonid V. Kovalev","doi":"arxiv-2407.12572","DOIUrl":null,"url":null,"abstract":"We obtain a sharp bound on the number of self-intersections of a closed\nplanar curve with trigonometric parameterization. Moreover, we show that a\ngeneric curve of this form is normal in the sense of Whitney.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A sharp bound on the number of self-intersections of a trigonometric curve\",\"authors\":\"Sergei Kalmykov, Leonid V. Kovalev\",\"doi\":\"arxiv-2407.12572\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We obtain a sharp bound on the number of self-intersections of a closed\\nplanar curve with trigonometric parameterization. Moreover, we show that a\\ngeneric curve of this form is normal in the sense of Whitney.\",\"PeriodicalId\":501142,\"journal\":{\"name\":\"arXiv - MATH - Complex Variables\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Complex Variables\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.12572\",\"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 - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.12572","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A sharp bound on the number of self-intersections of a trigonometric curve
We obtain a sharp bound on the number of self-intersections of a closed
planar curve with trigonometric parameterization. Moreover, we show that a
generic curve of this form is normal in the sense of Whitney.