The Curve Shortening Flow in the Metric-Affine Plane

被引：0
|
作者：
Rovenski, Vladimir [1 ]
机构：
[1] Univ Haifa, Dept Math, IL-31905 Haifa, Israel
来源：
MATHEMATICS | 2020年 / 8卷 / 05期
关键词：
curve shortening flow; affine connection; curvature; convex;
D O I：
10.3390/math8050701
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigated, for the first time, the curve shortening flow in the metric-affine plane and prove that under simple geometric condition (when the curvature of initial curve dominates the torsion term) it shrinks a closed convex curve to a "round point" in finite time. This generalizes the classical result by M. Gage and R.S. Hamilton about convex curves in a Euclidean plane.
引用
收藏
页数：11
相关论文
共 50 条
  • [1] Grid Peeling and the Affine Curve-Shortening Flow
    Eppstein, David
    Har-Peled, Sariel
    Nivasch, Gabriel
    EXPERIMENTAL MATHEMATICS, 2020, 29 (03) : 306 - 316
  • [2] A HIGHER ORDER SCHEME FOR THE CURVE SHORTENING FLOW OF PLANE CURVES
    Balazovjech, Martin
    Mikula, Karol
    ALGORITMY 2009: 18TH CONFERENCE ON SCIENTIFIC COMPUTING, 2009, : 165 - 175
  • [3] Harnack Inequality for Equi-Affine Curve Shortening Flow
    Yu Y.-H.
    Jin L.
    Dongbei Daxue Xuebao/Journal of Northeastern University, 2022, 43 (01): : 147 - 152
  • [4] Exactly solvable connections in metric-affine gravity
    Iosifidis, Damianos
    CLASSICAL AND QUANTUM GRAVITY, 2019, 36 (08)
  • [5] On parity-odd sector in metric-affine theories
    Jimenez, Jose Beltran
    Jimenez-Cano, Alejandro
    Obukhov, Yuri N.
    EUROPEAN PHYSICAL JOURNAL C, 2023, 83 (02):
  • [6] Affine self-similar solutions of the affine curve shortening flow I: The degenerate case
    Yu, Chengjie
    Zhao, Feifei
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 285 : 686 - 713
  • [7] On the topological character of metric-affine Lovelock Lagrangians in critical dimensions
    Janssen, Bert
    Jimenez-Cano, Alejandro
    PHYSICS LETTERS B, 2019, 798
  • [8] A HIGHER ORDER SCHEME FOR A TANGENTIALLY STABILIZED PLANE CURVE SHORTENING FLOW WITH A DRIVING FORCE
    Balazovjech, Martin
    Mikula, Karol
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2011, 33 (05) : 2277 - 2294
  • [9] Sharp entropy bounds for plane curves and dynamics of the curve shortening flow
    Baldauf, Julius
    Sun, Ao
    COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2023, 31 (03) : 595 - 624
  • [10] The Mixed Scalar Curvature of Almost-Product Metric-Affine Manifolds
    Rovenski, Vladimir
    Zawadzki, Tomasz
    RESULTS IN MATHEMATICS, 2018, 73 (01)
12345