Paper · Jul 14, 2016

Isometrische Einbettung von geschlossenen Riemannschen Mannigfaltigkeiten

Norman Zergänge

math.DGarXiv:1607.04259
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Abstract

In this work we give a detailed description of Matthias Günther's proof of the Isometric Embedding Theorem of Riemannian manifolds. Subsequently we will use this method to show that it is possible to construct an isometric embedding of a geometric flow, for instance the Ricci-flow, into some Euclidean space.

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Submitted
Jul 14, 2016
Subjects
math.DG, math.AP

Comments: This is the author's Diplomarbeit written in 2013, in German

Ricci flow

Its neighbourhood

Connected papers

The 4 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.

Connected papers This paper in the centre and the 4 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Convergence of Riemannian 4-manifolds with L²-curvature bounds (Norman Zergänge, 2017)3Zergänge 2017 Einstein solvmanifolds as submanifolds of symmetric spaces (Michael Jablonski, 2018)2Jablonski 2018 Negatively Curved Three-Manifolds, Hyperbolic Metrics, Isometric Embeddings In Minkowski Space And The Cross Curvature Flow (Paul Bryan, Mohammad N. Ivaki and Julian Scheuer, 2019)1Bryan 2019 Universal embeddings of flag manifolds and rigidity phenomena (Andrea Loi, Roberto Mossa and Fabio Zuddas, 2025)4Loi 2025
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Negatively Curved Three-Manifolds, Hyperbolic Metrics, Isometric Embeddings In Minkowski Space And The Cross Curvature Flow

    Paul Bryan, Mohammad N. Ivaki and Julian Scheuer

    Shared terms “isometric embedding”

  2. Einstein solvmanifolds as submanifolds of symmetric spaces

    Michael Jablonski

    Shared terms “isometric embedding”, “embedding theorem”

  3. Convergence of Riemannian -manifolds with -curvature bounds

    Norman ZergängeWider flows

    Same author Norman Zergänge · Shared terms “Euclidean”

  4. Universal embeddings of flag manifolds and rigidity phenomena

    Andrea Loi, Roberto Mossa and Fabio Zuddas

    Shared terms “embedding”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci flow Hamilton's Ricci flow evolves a Riemannian metric by minus twice its Ricci curvature. It is a nonlinear heat equation for geometry: it spreads… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982)

In the guidebook

  1. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.

  2. 10A.12
    Curve Shortening and Minimal DiscsBook 10A · Three-Manifolds and Geometrization

    How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.

  3. 11A.1
    The Equation and Its First SolutionsBook 11A · The Ricci Flow: Existence and Maximum Principles

    A heat equation for the metric: spheres, cylinders and scaling.