Paper · Dec 4, 2023

Flows of piecewise analytic vector fields in convex polytope decompositions

Tianqi Wu

math.GTWider flowsarXiv:2312.01698
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Abstract

We prove that for a convex polytope decomposition of a domain in , an integral curve of a piecewise analytic vector field is chopped by the decomposition into finitely many pieces. As a consequence, we prove the finiteness of the number of the edge flips in a discrete Yamabe flow.

Yamabe flow

Its neighbourhood

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The 8 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 2021, plus the canon.

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Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant

    Gilles Carron, Eric Chen and Yi WangWider flows PDF

    Topics Yamabe flow

  2. Gap Theorem on locally conformally flat manifold

    Ming Hsiao and Man-Chun LeeWider flows PDF

    Topics Yamabe flow

  3. A non-convergence phenomenon for the CR Yamabe flow

    Claudio Afeltra, Andrea Pinamonti and Pak Tung HoWider flows PDF

    Topics Yamabe flow

  4. Combinatorial Yamabe flow on hyperbolic bordered surfaces

    Shengyu Li, Xu Xu and Ze ZhouWider flows PDF

    Topics Yamabe flow

  5. Convergence rate of the weighted Yamabe flow

    Pak Tung Ho, Jinwoo Shin and Zetian YanWider flows PDF

    Topics Yamabe flow

  6. Generalized Yamabe Flows

    Jørgen Olsen Lye, Boris Vertman and Mannaim Gennaro VittiWider flows PDF

    Topics Yamabe flow

  7. A note on the Chern-Yamabe flow on compact Hermitian manifolds with negative Gauduchon degree

    Weike YuWider flows PDF

    Topics Yamabe flow

  8. A dual Yamabe flow and related integral flows

    Jingang XiongWider flows PDF

    Topics Yamabe flow

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.

Yamabe flow Wider flows The Yamabe flow deforms a metric within its conformal class, driven by scalar curvature. It is a parabolic approach to the Yamabe problem: find a… Start with: The yamabe flow on locally conformally flat manifolds with positive ricci curvature (Chow, 1992)

In the guidebook

  1. 6C.4
    The Yamabe Problem and Critical ExponentsBook 6C · Nonlinear PDE: Variational and Geometric Methods

    Conformal changes of scalar curvature, the Yamabe functional, Aubin's threshold and Schoen's solution, concentration compactness and bubbles, and why Perelman's log-Sobolev minimisers always exist.