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  A novel type of Sobolev-Poincare inequality for submanifolds of Euclidean space

Menne, U., & Scharrer, C. (submitted). A novel type of Sobolev-Poincare inequality for submanifolds of Euclidean space.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002E-07B5-8 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-F779-0
Genre: Paper

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1709.05504.pdf (Preprint), 877KB
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 Creators:
Menne, Ulrich, Author
Scharrer, Christian1, Author
Affiliations:
1AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24008              

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Free keywords: Mathematics, Differential Geometry, math.DG,Mathematics, Analysis of PDEs, math.AP,Mathematics, Classical Analysis and ODEs, math.CA,
 Abstract: For functions on generalised connected surfaces (of any dimensions) with boundary and mean curvature, we establish an oscillation estimate in which the mean curvature enters in a novel way. As application we prove an a priori estimate of the geodesic diameter of compact connected smooth immersions in terms of their boundary data and mean curvature. These results are developed in the framework of varifolds. For this purpose, we establish that the notion of indecomposability is the appropriate substitute for connectedness and that it has a strong regularising effect; we thus obtain a new natural class of varifolds to study. Finally, our development leads to a variety of questions that are of substance both in the smooth and the nonsmooth setting.

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 Dates: 2017-09-162017
 Publication Status: Submitted
 Pages: 35 pages, no figures
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1709.05504
URI: http://arxiv.org/abs/1709.05504
 Degree: -

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