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Sat, 12 Jan 2008 09:05:51 +0100Sat, 12 Jan 2008 09:05:51 +0100Measure and Integration on Lipschitz-Manifolds
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/426
The first part of this paper is concerned with various definitions of a k-dimensional Lipschitz-manifold and a discussion of the equivalence of these definitions. The second part is then devoted to the geometrically intrinsic construction of a sigma-algebra L of subsets of the manifold and a measure on L.Joachim Naumann; Christian G. Simaderworkingpaperhttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/426Mon, 01 Dec 2008 09:05:51 +0100A homotopy argument and its applications to the transformation rule for bi-Lipschitz mappings, the Brouwer fixed point theorem and the Brouwer degree
http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/222
The main purpose of the paper is to present an elementary self-contained proof of the change of variables formula for injective, locally bi-Lipschitz mappings. The proof is based on a homotopy argument. Various properties of bi-Lipschitz mappings are studied. As a by-product Lipschitz variants of the classical implicit function theorem and the local diffeomorphism theorem are proved. With the help of the homotopy argument a simple proof is given of Brouwer’s fixed point theorem and the main properties of Brouwer’s degree of mapping.Christian G. Simaderpreprinthttp://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/222Thu, 07 Sep 2006 11:25:42 +0200