Add to ORKG©1998 American Mathematical Society. First published in Journal of the American Mathematical Society, Vol. 11, No. 3, July 1998; published by the American Mathematical Society.DOI: 10.1090/S0894-0347-98-00262-8In this paper, we extend to the non-convex case the affine invariant geometric heat equation studied by Sapiro and Tannenbaum for convex plane curves. We prove that a smooth embedded plane curve will converge to a point when evolving according to this flow. This result extends the analogy between the affine heat equation and the well-known Euclidean geometric heat equation
This article is a general introduction to Cartan's moving frame method which is elegant, simple and ...
summary:In a crystalline algorithm, a tangential velocity is used implicitly. In this short note, it...
In this paper, we will investigate a new curvature flow for closed convex plane curves which shorten...
In Euclidean geometry, the shortest distance between two points is a straight line. Chern made a con...
AbstractAn affine invariant curve evolution process is presented in this work. The evolution studied...
AbstractAn affine invariant curve evolution process is presented in this work. The evolution studied...
We study the effects of a deformation via the heat equation on closed, plane curves. We begin with a...
In this paper, the isoperimetric inequality in centro-affine plane geometry is obtained. We also inv...
The motion of any smooth closed convex curve in the plane in the direction of steepest increase of i...
A geometric evolution equation is a partial differential equation that evolves some kind of geometri...
AbstractA new geometric approach to the affine geometry of curves in the plane and to affine-invaria...
AbstractThe long time behavior of a curve in the whole plane moving by a curvature flow is studied. ...
We establish the geometric origin ot the nonlinear heat equation with arct-angential nonlinearity: ∂...
We study afliue iuvariauts of plauc curves from the view point of the singularity theory of smooth ...
©1993 SPIE--The International Society for Optical Engineering. One print or electronic copy may be m...
This article is a general introduction to Cartan's moving frame method which is elegant, simple and ...
summary:In a crystalline algorithm, a tangential velocity is used implicitly. In this short note, it...
In this paper, we will investigate a new curvature flow for closed convex plane curves which shorten...
In Euclidean geometry, the shortest distance between two points is a straight line. Chern made a con...
AbstractAn affine invariant curve evolution process is presented in this work. The evolution studied...
AbstractAn affine invariant curve evolution process is presented in this work. The evolution studied...
We study the effects of a deformation via the heat equation on closed, plane curves. We begin with a...
In this paper, the isoperimetric inequality in centro-affine plane geometry is obtained. We also inv...
The motion of any smooth closed convex curve in the plane in the direction of steepest increase of i...
A geometric evolution equation is a partial differential equation that evolves some kind of geometri...
AbstractA new geometric approach to the affine geometry of curves in the plane and to affine-invaria...
AbstractThe long time behavior of a curve in the whole plane moving by a curvature flow is studied. ...
We establish the geometric origin ot the nonlinear heat equation with arct-angential nonlinearity: ∂...
We study afliue iuvariauts of plauc curves from the view point of the singularity theory of smooth ...
©1993 SPIE--The International Society for Optical Engineering. One print or electronic copy may be m...
This article is a general introduction to Cartan's moving frame method which is elegant, simple and ...
summary:In a crystalline algorithm, a tangential velocity is used implicitly. In this short note, it...
In this paper, we will investigate a new curvature flow for closed convex plane curves which shorten...