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    <pubDate>Sun, 09 Jul 2006 11:25:42 +0200</pubDate>
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      <title>A homotopy argument and its applications to the transformation rule for bi-Lipschitz mappings, the Brouwer fixed point theorem and the Brouwer degree</title>
      <link>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/222</link>
      <description>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.</description>
      <author>Christian G. Simader</author>
      <category>preprint</category>
      <guid>http://opus4.kobv.de/opus4-ubbayreuth/frontdoor/index/index/docId/222</guid>
      <pubDate>Thu, 07 Sep 2006 11:25:42 +0200</pubDate>
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