{"title":"由单调凸函数生成的旋转表面上的曲线缩短流","authors":"Naotoshi FUJIHARA","doi":"10.2206/kyushujm.77.179","DOIUrl":null,"url":null,"abstract":"In this paper, we study curve shortening flows on rotational surfaces in ℝ3. We assume that the surfaces have negative Gauss curvatures and that some condition related to the Gauss curvature and the curvature of an embedded curve holds on them. Under these assumptions, we prove that the curve remains a graph over the parallels of the rotational surface along the flow. Also, we prove the comparison principle and the long-time existence of the flow.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"69 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"CURVE SHORTENING FLOWS ON ROTATIONAL SURFACES GENERATED BY MONOTONE CONVEX FUNCTIONS\",\"authors\":\"Naotoshi FUJIHARA\",\"doi\":\"10.2206/kyushujm.77.179\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study curve shortening flows on rotational surfaces in ℝ3. We assume that the surfaces have negative Gauss curvatures and that some condition related to the Gauss curvature and the curvature of an embedded curve holds on them. Under these assumptions, we prove that the curve remains a graph over the parallels of the rotational surface along the flow. Also, we prove the comparison principle and the long-time existence of the flow.\",\"PeriodicalId\":49929,\"journal\":{\"name\":\"Kyushu Journal of Mathematics\",\"volume\":\"69 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kyushu Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2206/kyushujm.77.179\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyushu Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2206/kyushujm.77.179","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
CURVE SHORTENING FLOWS ON ROTATIONAL SURFACES GENERATED BY MONOTONE CONVEX FUNCTIONS
In this paper, we study curve shortening flows on rotational surfaces in ℝ3. We assume that the surfaces have negative Gauss curvatures and that some condition related to the Gauss curvature and the curvature of an embedded curve holds on them. Under these assumptions, we prove that the curve remains a graph over the parallels of the rotational surface along the flow. Also, we prove the comparison principle and the long-time existence of the flow.
期刊介绍:
The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total.
More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.