Peano curves with smooth footprints

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• 作者：Jairo Bochi ; Pedro H. Milet
• 刊名：Monatshefte f¨¹r Mathematik
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：180
• 期：4
• 页码：693-712
• 全文大小：602 KB
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081
• 卷排序：180

文摘

We construct Peano curves \(\gamma : [0,\infty ) \rightarrow \mathbb {R}^2\) whose “footprints” \(\gamma ([0,t])\), \(t>0\), have \(C^\infty \) boundaries and are tangent to a common continuous line field on the punctured plane \(\mathbb {R}^2 {\backslash }\{\gamma (0)\}\). Moreover, these boundaries can be taken \(C^\infty \)-close to any prescribed smooth family of nested smooth Jordan curves contracting to a point.KeywordsSpace-filling curvesSmoothnessConvexityLine fields