Paper · Jun 5, 2016

Neumann boundary value problem for gernera curvature flow with forcing term

Ling Xiao

math.DGWider flowsarXiv:1606.01580
View PDF View HTML arXiv page

As on arXiv

Abstract

In this paper, we prove long time existence and convergence results for a class of general curvature flows with Neumann boundary condition. This is the first result for the Neumann boundary problem of non Monge-Ampere type curvature equations. Our method also works for the corresponding elliptic setting.

View PDF View HTML arXiv page
Submitted
Jun 5, 2016
Subjects
math.DG, math.AP
Other curvature flowsKähler geometryBoundaries & non-compactFree boundary & capillaryLong-time existence & convergence

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 General curvature flow without singularities (Ling Xiao, 2016)6Xiao 2016 Mean Curvature Flows of Graphs with Neumann Boundary condition (Jinju Xu, 2016)1Xu 2016 A remark on gradient estimates for spacelike mean curvature flow with boundary conditions (Ben Lambert, 2016)8Lambert 2016 Higher order curvature flows of plane curves with generalised Neumann boundary conditions (James McCoy, Glen Wheeler and Yuhan Wu, 2020)2McCoy 2020 Level set mean curvature flow with Neumann boundary conditions (Satoru Aimi, 2021)3Aimi 2021 Level-set forced mean curvature flow with the Neumann boundary condition (Jiwoong Jang, Dohyun Kwon, Hiroyoshi Mitake et al., 2021)5Jang 2021 Mean curvature flow of graphs in Generalized Robertson-Walker spacetimes with perpendicular Neumann boundary condition (Jorge Lira and Fernanda Roing, 2022)4Lira 2022 Anisotropic mean curvature flow with contact angle and Neumann boundary conditions in arbitrary dimensions (Can Cui and Nung Kwan Yip, 2025)7Cui 2025
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Mean Curvature Flows of Graphs with Neumann Boundary condition

    Jinju XuWider flows

    Topics Free boundary & capillary, Boundaries & non-compact · Shared terms “Neumann boundary”, “boundary condition”

  2. Higher order curvature flows of plane curves with generalised Neumann boundary conditions

    James McCoy, Glen Wheeler and Yuhan WuWider flows

    Topics Free boundary & capillary, Long-time existence & convergence, Boundaries & non-compact · Shared terms “Neumann boundary”, “boundary condition”

  3. Level set mean curvature flow with Neumann boundary conditions

    Satoru AimiWider flows

    Topics Free boundary & capillary, Boundaries & non-compact · Shared terms “Neumann boundary”, “boundary condition”

  4. Mean curvature flow of graphs in Generalized Robertson-Walker spacetimes with perpendicular Neumann boundary condition

    Jorge Lira and Fernanda RoingWider flows

    Topics Free boundary & capillary, Long-time existence & convergence, Boundaries & non-compact · Shared terms “Neumann boundary”, “boundary condition”

  5. Level-set forced mean curvature flow with the Neumann boundary condition

    Jiwoong Jang, Dohyun Kwon, Hiroyoshi Mitake et al.Wider flows

    Topics Free boundary & capillary, Boundaries & non-compact · Shared terms “Neumann boundary”, “forcing term”, “boundary condition”

  6. General curvature flow without singularities

    Ling XiaoWider flows

    Topics Long-time existence & convergence, Boundaries & non-compact, Other curvature flows · Same author Ling Xiao · Shared terms “boundary condition”

  7. Anisotropic mean curvature flow with contact angle and Neumann boundary conditions in arbitrary dimensions

    Can Cui and Nung Kwan YipWider flows

    Topics Free boundary & capillary, Boundaries & non-compact · Shared terms “Neumann boundary”, “boundary condition”

  8. A remark on gradient estimates for spacelike mean curvature flow with boundary conditions

    Ben LambertWider flows

    Topics Free boundary & capillary, Long-time existence & convergence, Boundaries & non-compact · Shared terms “Neumann boundary”, “boundary condition”

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) Kähler geometry Complex manifolds with compatible Riemannian metrics whose Kähler form is closed. Here Ricci curvature is the complex Hessian of a log-determinant… Start with: On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I (Yau, 1978) Boundaries & non-compact Ricci flow beyond closed manifolds: complete non-compact spaces, manifolds with boundary, and asymptotically flat or hyperbolic ends. Start with: Deforming the metric on complete Riemannian manifolds (Shi, 1989) Free boundary & capillary Flows whose boundary is free to slide on a support surface, meeting it at a right angle (free boundary) or at a fixed angle (capillary). Start with: Non-parametric mean curvature evolution with boundary conditions (Huisken, 1989)