Add to ORKGWe consider a closed surface in $\mathbb{R}^3$ evolving by the volume-preserving Willmore flow and prove a lower bound for the existence time of smooth solutions. For spherical initial surfaces with Willmore energy below $8\pi$ we show long time existence and convergence to a round sphere by performing a suitable blow-up and by proving a constrained Lojasiewicz-Simon inequality.Comment: 46 pages. Minor corrections and fixing of some typos. Convergence threshold in Thm. 1.2 now includes the equality case. Comments are welcome
We use the minimizing movement theory to study the gradient flow associated with a non-regular relax...
The goal of the present note is to survey and announce recent results by the authors about existence...
Abstract: A new formulation for the Euler-Lagrange equation of the Will-more functional for immersed...
We introduce a parametric framework for the study of Willmore gradient flows which enables to consid...
For a hypersurface in ${\mathbb R}^3$, Willmore flow is defined as the $L^2$--gradient flow of the c...
A new formulation for the Euler-Lagrange equation of the Willmore functional for immersed surfaces i...
Let (M, g) be a 3-dimensional Riemannian manifold. The goal of the paper it to show that if P0 ∈ M ...
In this paper we classify branched Willmore spheres with at most three branch points (including mult...
In this paper we prove a convergence result for sequences of Willmore immersions with simple minimal...
In this article, we prove two "global existence and full convergence theorems" for flow lines of the...
We consider the surface diffusion and Willmore flows acting on a general class of (possibly non–comp...
Geometric gradient flows of energy functionals involving the curvature of a given object have become...
We show the short-time existence and uniqueness of solutions for the motion of an evolving hypersurf...
"Regularity and Singularity for Partial Differential Equations with Conservation Laws". June 3～5, 20...
The well-posedness of a phase-field approximation to the Willmore flow with area and volume constrai...
We use the minimizing movement theory to study the gradient flow associated with a non-regular relax...
The goal of the present note is to survey and announce recent results by the authors about existence...
Abstract: A new formulation for the Euler-Lagrange equation of the Will-more functional for immersed...
We introduce a parametric framework for the study of Willmore gradient flows which enables to consid...
For a hypersurface in ${\mathbb R}^3$, Willmore flow is defined as the $L^2$--gradient flow of the c...
A new formulation for the Euler-Lagrange equation of the Willmore functional for immersed surfaces i...
Let (M, g) be a 3-dimensional Riemannian manifold. The goal of the paper it to show that if P0 ∈ M ...
In this paper we classify branched Willmore spheres with at most three branch points (including mult...
In this paper we prove a convergence result for sequences of Willmore immersions with simple minimal...
In this article, we prove two "global existence and full convergence theorems" for flow lines of the...
We consider the surface diffusion and Willmore flows acting on a general class of (possibly non–comp...
Geometric gradient flows of energy functionals involving the curvature of a given object have become...
We show the short-time existence and uniqueness of solutions for the motion of an evolving hypersurf...
"Regularity and Singularity for Partial Differential Equations with Conservation Laws". June 3～5, 20...
The well-posedness of a phase-field approximation to the Willmore flow with area and volume constrai...
We use the minimizing movement theory to study the gradient flow associated with a non-regular relax...
The goal of the present note is to survey and announce recent results by the authors about existence...
Abstract: A new formulation for the Euler-Lagrange equation of the Will-more functional for immersed...