Convex ancient solutions to curve shortening flow
نویسندگان
چکیده
منابع مشابه
Curve Shortening Flow in a Riemannian Manifold
In this paper, we systemally study the long time behavior of the curve shortening flow in a closed or non-compact complete locally Riemannian symmetric manifold. Assume that we have a global flow. Then we can exhibit a a limit for the global behavior of the flow. In particular, we show the following results. 1). Let M be a compact locally symmetric space. If the curve shortening flow exists for...
متن کاملAncient Solutions to Kähler-ricci Flow
In this paper, we prove that any non-flat ancient solution to KählerRicci flow with bounded nonnegative bisectional curvature has asymptotic volume ratio zero. We also classify all complete gradient shrinking solitons with nonnegative bisectional curvature. Both results generalize the corresponding earlier results of Perelman in [P1] and [P2]. The results then are applied to study the geometry ...
متن کاملThe Blow up Analysis of Solutions of the General Curve Shortening Flow
In this paper, a detailed asymptotic behavior of the closed curves is presented when they contract to a point in finite time under the general curve shortening flow.
متن کاملResults of Triangles Under Discrete Curve Shortening Flow
In this paper, we analyze the results of triangles under discrete curve shortening flow, specifically isosceles triangles with top angles greater than π3 , and scalene triangles. By considering the location of the three vertices of the triangle after some small time , we use the definition of the derivative to calculate a system of differential equations involving parameters that can describe t...
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: Calculus of Variations and Partial Differential Equations
سال: 2020
ISSN: 0944-2669,1432-0835
DOI: 10.1007/s00526-020-01784-8