Lipschitz images with fractal boundaries and their small surface wrapping期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Lipschitz images with fractal boundaries and their small surface wrapping

Authors:	Zoltá n Buczolich

Affiliation:	Eötvös Loránd University, Department of Analysis, Budapest, Múzeum krt 6-8, H-1088, Hungary

Abstract:	Assume $Esubset Hsubset mathbf{R}^{m}$ and $Phi :Eto mathbf{R}^{m}$ is a Lipschitz -mapping; and denote the volume and the surface area of . We verify that there exists a figure with $\|\|F\|\|leq c_{L} \|\|H\|\|$ , and, of course, $\|F\|leq c_{L} \|H\|$ , where $c_{L}$ depends only on the dimension and on . We also give an example when $E=Hsubset mathbf{R}^{2}$ is a square and ; in fact, the boundary of can contain a fractal of Hausdorff dimension exceeding one.

Keywords:	Lipschitz mapping surface fractal

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