The Curve Shortening Flow in the Metric-Affine Plane
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 classica...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-05-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/8/5/701 |
| _version_ | 1797569051692630016 |
|---|---|
| author | Vladimir Rovenski |
| author_facet | Vladimir Rovenski |
| author_sort | Vladimir Rovenski |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T20:05:33Z |
| format | Article |
| id | doaj.art-7e7b943f324e4da5bec7ec5b29ef0ee5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:05:33Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7e7b943f324e4da5bec7ec5b29ef0ee52023-11-19T23:19:56ZengMDPI AGMathematics2227-73902020-05-018570110.3390/math8050701The Curve Shortening Flow in the Metric-Affine PlaneVladimir Rovenski0Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, IsraelWe 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.https://www.mdpi.com/2227-7390/8/5/701curve shortening flowaffine connectioncurvatureconvex |
| spellingShingle | Vladimir Rovenski The Curve Shortening Flow in the Metric-Affine Plane Mathematics curve shortening flow affine connection curvature convex |
| title | The Curve Shortening Flow in the Metric-Affine Plane |
| title_full | The Curve Shortening Flow in the Metric-Affine Plane |
| title_fullStr | The Curve Shortening Flow in the Metric-Affine Plane |
| title_full_unstemmed | The Curve Shortening Flow in the Metric-Affine Plane |
| title_short | The Curve Shortening Flow in the Metric-Affine Plane |
| title_sort | curve shortening flow in the metric affine plane |
| topic | curve shortening flow affine connection curvature convex |
| url | https://www.mdpi.com/2227-7390/8/5/701 |
| work_keys_str_mv | AT vladimirrovenski thecurveshorteningflowinthemetricaffineplane AT vladimirrovenski curveshorteningflowinthemetricaffineplane |