Motion of Level Set by General Curvature
نویسنده
چکیده
In this paper, we study the motion of level sets by general curvature. The difficulty in this setting is for a general curvature function, it’s only well defined in an admissible cone. In order to extend the existence result to outside the cone we introduce a new approximation function f̂ (see (3.1)). Moreover, using the idea in [5], we give an elliptic approach for the Ben-Andrews’ non-collapsing result in fully nonlinear curvature flows. We hope this approach can be generalized to a wider class of elliptic equations.
منابع مشابه
Piecewise Constant Level Set Method for Multiphase Motion
Abstract. We apply the Piecewise Constant Level Set Method (PCLSM) to a multiphase motion problem, especially the pure mean curvature motion. We use one level set function to represent multiple regions, and by associating an energy functional which consists of surface tension (proportional to length), we formulate a variational approach for the mean curvature motion problem. Some operator-split...
متن کاملPiecewise Constant Level Set Methods for Multiphase Motion
We apply the Piecewise Constant Level Set Method (PCLSM) to a multiphase motion problem, especially the pure mean curvature motion. We use one level set function to represent multiple regions, and by associating an energy functional which consists of surface tension (proportional to length), we formulate a variational approach for the mean curvature motion problem. Some operator-splitting schem...
متن کاملMotion of Level Sets by Mean Curvature. I
We construct a unique weak solution of the nonlinear PDE which asserts each level set evolves in time according to its mean curvature. This weak solution allows us then to define for any compact set Γo a unique generalized motion by mean curvature, existing for all time. We investigate the various geometric properties and pathologies of this evolution.
متن کاملA Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems
We propose a new semi-implicit level set approach to a class of curvature dependent flows. The method generalizes a recent algorithm proposed for the motion by mean curvature where the interface is updated by solving the Rudin-Osher-Fatemi (ROF) model for image regularization. Our proposal is general enough so that one can easily extend and apply the method to other curvature dependent motions....
متن کاملOn Level Set Formulations for Anisotropic Mean Curvature Flow and Surface Diffusion
Anisotropic mean curvature motion and in particular anisotropic surface diffusion play a crucial role in the evolution of material interfaces. This evolution interacts with conservations laws in the adjacent phases on both sides of the interface and are frequently expected to undergo topological chances. Thus, a level set formulation is an appropriate way to describe the propagation. Here we re...
متن کامل