Andrea Pinamonti , Gareth Speight , Scott Zimmerman
{"title":"海森堡群中水平曲线的高阶惠特尼扩展和卢辛近似","authors":"Andrea Pinamonti , Gareth Speight , Scott Zimmerman","doi":"10.1016/j.matpur.2024.06.005","DOIUrl":null,"url":null,"abstract":"<div><p>In the setting of horizontal curves in the Heisenberg group, we prove a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>ω</mi></mrow></msup></math></span> finiteness principle, a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>ω</mi></mrow></msup></math></span> Lusin approximation result, a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> Whitney extension result, and a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>, <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>ω</mi></mrow></msup></math></span>, and <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> in the Heisenberg group.</p></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021782424000801/pdfft?md5=f47e1c136eb6a58b1e26a2db9f54d4d9&pid=1-s2.0-S0021782424000801-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Higher order Whitney extension and Lusin approximation for horizontal curves in the Heisenberg group\",\"authors\":\"Andrea Pinamonti , Gareth Speight , Scott Zimmerman\",\"doi\":\"10.1016/j.matpur.2024.06.005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the setting of horizontal curves in the Heisenberg group, we prove a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>ω</mi></mrow></msup></math></span> finiteness principle, a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>ω</mi></mrow></msup></math></span> Lusin approximation result, a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> Whitney extension result, and a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>, <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>ω</mi></mrow></msup></math></span>, and <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> in the Heisenberg group.</p></div>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0021782424000801/pdfft?md5=f47e1c136eb6a58b1e26a2db9f54d4d9&pid=1-s2.0-S0021782424000801-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021782424000801\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021782424000801","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Higher order Whitney extension and Lusin approximation for horizontal curves in the Heisenberg group
In the setting of horizontal curves in the Heisenberg group, we prove a finiteness principle, a Lusin approximation result, a Whitney extension result, and a Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class , , and in the Heisenberg group.
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