Paper · Mar 10, 2020

Extrinsic curvature flows and applications

Julian Scheuer

math.DGWider flowsarXiv:2003.04482
View PDF View HTML arXiv page

As on arXiv

Abstract

These notes arose from a mini lecture series the author gave at the Early Career Researchers Workshop on Geometric Analysis and PDEs, held in January 2020 at the Matrix institute of the University of Melbourne. We discussed some classical aspects of expanding curvature flows and obtained first applications. In these notes we will give a detailed account on what was covered during the lectures.

View PDF View HTML arXiv page
Submitted
Mar 10, 2020
Subjects
math.DG, math.AP
Journal
MATRIX Book series 4, Wood, de Gier, Praeger, Tao (eds.), Springer (2021), p. 747-772
DOI
10.1007/978-3-030-62497-2
Other curvature flows

Its neighbourhood

Connected papers

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 2016, plus the canon.

Connected papers This paper in the centre and the 8 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 On the classification of ancient solutions to curvature flows on the sphere (Paul Bryan, Mohammad N. Ivaki and Julian Scheuer, 2016)6Bryan 2016 A unified flow approach to smooth, even Lₚ-Minkowski problems (Paul Bryan, Mohammad N. Ivaki and Julian Scheuer, 2016)1Bryan 2016 Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature (Heiko Kröner and Julian Scheuer, 2017)4Kröner 2017 Inverse curvature flows in Riemannian warped products (Julian Scheuer, 2017)2Scheuer 2017 Lectures on curvature flow of networks (Carlo MAntegazza, Matteo Novaga and Alessandra Pluda, 2019)3MAntegazza 2019 Parabolic approaches to curvature equations (Paul Bryan, Mohammad N. Ivaki and Julian Scheuer, 2020)8Bryan 2020 Christoffel-Minkowski flows (Paul Bryan, Mohammad N. Ivaki and Julian Scheuer, 2020)5Bryan 2020 Capillary quermassintegral inequalities in the unit ball (Shujing Pan and Julian Scheuer, 2026)7Pan 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. A unified flow approach to smooth, even -Minkowski problems

    Paul Bryan, Mohammad N. Ivaki and Julian ScheuerWider flows

    Topics Other curvature flows · Same author Julian Scheuer · Shared terms “expanding curvature”

  2. Inverse curvature flows in Riemannian warped products

    Julian ScheuerWider flows

    Topics Other curvature flows · Same author Julian Scheuer · Shared terms “expanding curvature”

  3. Lectures on curvature flow of networks

    Carlo MAntegazza, Matteo Novaga and Alessandra PludaWider flows

    Topics Other curvature flows

  4. Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

    Heiko Kröner and Julian ScheuerWider flows

    Topics Other curvature flows · Same author Julian Scheuer · Shared terms “expanding curvature”

  5. Christoffel-Minkowski flows

    Paul Bryan, Mohammad N. Ivaki and Julian ScheuerWider flows

    Topics Other curvature flows · Same author Julian Scheuer

  6. On the classification of ancient solutions to curvature flows on the sphere

    Paul Bryan, Mohammad N. Ivaki and Julian ScheuerWider flows

    Topics Other curvature flows · Same author Julian Scheuer

  7. Capillary quermassintegral inequalities in the unit ball

    Shujing Pan and Julian ScheuerWider flows

    Topics Other curvature flows · Same author Julian Scheuer

  8. Parabolic approaches to curvature equations

    Paul Bryan, Mohammad N. Ivaki and Julian ScheuerWider flows

    Topics Other curvature flows · Same author Julian Scheuer

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.

Other curvature flows Wider flows Flows that move a hypersurface or metric by some other function of curvature: Gauss curvature (worn stones), inverse mean curvature (the Penrose… Start with: Shapes of worn stones (Firey, 1974)