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Mean Curvature Flow (mean + curvature_flow)
Selected AbstractsMean curvature flows and isotopy of maps between spheresCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2004Mao-Pei Tsui Let f be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions. A corollary is that any area-decreasing map between unit spheres (of possibly different dimensions) is isotopic to a constant map. © 2004 Wiley Periodicals, Inc. [source] Anisotropic curve shortening flow in higher codimensionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2007Paola Pozzi Abstract We consider the evolution of parametric curves by anisotropic mean curvature flow in ,n for an arbitrary n,2. After the introduction of a spatial discretization, we prove convergence estimates for the proposed finite-element model. Numerical tests and simulations based on a fully discrete semi-implicit stable algorithm are presented. Copyright © 2007 John Wiley & Sons, Ltd. [source] A direct method for solving an anisotropic mean curvature flow of plane curves with an external forceMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2004Karol Mikula Abstract A new method for solution of the evolution of plane curves satisfying the geometric equation v=,(x,k,,), where v is the normal velocity, k and , are the curvature and tangential angle of a plane curve , , ,2 at the point x,,, is proposed. We derive a governing system of partial differential equations for the curvature, tangential angle, local length and position vector of an evolving family of plane curves and prove local in time existence of a classical solution. These equations include a non-trivial tangential velocity functional governing a uniform redistribution of grid points and thus preventing numerically computed solutions from forming various instabilities. We discretize the governing system of equations in order to find a numerical solution for 2D anisotropic interface motions and image segmentation problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Mean curvature flows and isotopy of maps between spheresCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 8 2004Mao-Pei Tsui Let f be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions. A corollary is that any area-decreasing map between unit spheres (of possibly different dimensions) is isotopic to a constant map. © 2004 Wiley Periodicals, Inc. [source] | ||||||||||