Diameter and curvature control under mean curvature flow
نویسندگان
چکیده
منابع مشابه
Mean Curvature Blowup in Mean Curvature Flow
In this note we establish that finite-time singularities of the mean curvature flow of compact Riemannian submanifolds M t →֒ (N, h) are characterised by the blow up of the mean curvature.
متن کاملNeck Pinching Dynamics Under Mean Curvature Flow
In this paper we study motion of surfaces of revolution under the mean curvature flow. For an open set of initial conditions close to cylindrical surfaces we show that the solution forms a “neck” which pinches in a finite time at a single point. We also obtain a detailed description of the neck pinching process.
متن کاملMean curvature flow
Mean curvature flow is the negative gradient flow of volume, so any hypersurface flows through hypersurfaces in the direction of steepest descent for volume and eventually becomes extinct in finite time. Before it becomes extinct, topological changes can occur as it goes through singularities. If the hypersurface is in general or generic position, then we explain what singularities can occur un...
متن کاملRiemannian Mean Curvature Flow
In this paper we explicitly derive a level set formulation for mean curvature flow in a Riemannian metric space. This extends the traditional geodesic active contour framework which is based on conformal flows. Curve evolution for image segmentation can be posed as a Riemannian evolution process where the induced metric is related to the local structure tensor. Examples on both synthetic and re...
متن کاملImage Processing: Flows under Min/Max Curvature and Mean Curvature
part, based on a local decision. This approach has several We present a class of PDE-based algorithms suitable for key virtues. First, it contains only one enhancement paramimage denoising and enhancement. The techniques are applicaeter, which in most cases is automatically chosen. Second, ble to both salt-and-pepper gray-scale noise and full-image the scheme automatically picks the stopping cr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2020
ISSN: 1080-6377
DOI: 10.1353/ajm.2020.0046