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Sun, 09 Jul 2006 11:25:42 +0200Sun, 09 Jul 2006 11:25:42 +0200A 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