Curve shortening flows in warped product manifolds
Copyright policy )Curve shortening flows in warped product manifolds
We study curve shortening flows in two types of warped product manifolds. These manifolds are $S^1\times N$ with two types of warped metrics where $S^1$ is the unit circle in $R^2$ and $N$ is a closed Riemannian manifold. If the initial curve is a graph over $S^1$, then its curve shortening flow exists for all times and finally converges to a geodesic closed curve.
Final Version. (The proof of Proposition 5.1 is revised). Accepted by Proceedings of AMS
- Sun Yat-sen University China (People's Republic of)
Mathematics - Differential Geometry, Differential Geometry (math.DG), warped product manifolds, General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Geodesics in global differential geometry, curve-shortening flow, Geometric evolution equations (mean curvature flow, Ricci flow, etc.), geodesic
Mathematics - Differential Geometry, Differential Geometry (math.DG), warped product manifolds, General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Geodesics in global differential geometry, curve-shortening flow, Geometric evolution equations (mean curvature flow, Ricci flow, etc.), geodesic
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!