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Uniformly Regular and Singular Riemannian Manifolds

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Book cover Elliptic and Parabolic Equations

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 119))

Abstract

A detailed study of uniformly regular Riemannian manifolds and manifolds with singular ends is carried out in this paper. Such classes of manifolds are of fundamental importance for a Sobolev space solution theory for parabolic evolution equations on noncompact Riemannian manifolds with and without boundary. Besides pointing out this connection in some detail we present large families of uniformly regular and singular manifolds which are admissible for this analysis.

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Notes

  1. 1.

    Precise definitions of all concepts used in this introduction without further explanation are found in the main body of this paper—in Sect. 2, in particular.

  2. 2.

    Cf. the localized definitions in Sect. 2.

  3. 3.

    More precisely: \({J=J_{\infty}}\) and \({R\in{\mathcal F}(J)}\).

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Author information

Authors and Affiliations

  1. Mathematical Institute, University of Zurich, Winterthurerstr. 190, 8057, Zürich, Switzerland

    Herbert Amann

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  1. Herbert Amann
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Correspondence to Herbert Amann .

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Editors and Affiliations

  1. Institute for Applied Mathematics, Leibniz University of Hannover, Hannover, Germany

    Joachim Escher

  2. Institute for Analysis, Leibniz University of Hannover, Hannover, Germany

    Elmar Schrohe

  3. Department of Mathematics, University of Torino, Torino, Torino, Italy

    Jörg Seiler

  4. Institute for Applied Mathematics, Leibniz University of Hannover, Hannover, Germany

    Christoph Walker

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Amann, H. (2015). Uniformly Regular and Singular Riemannian Manifolds. In: Escher, J., Schrohe, E., Seiler, J., Walker, C. (eds) Elliptic and Parabolic Equations. Springer Proceedings in Mathematics & Statistics, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-12547-3_1

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