## 321 Citations

Global existence and full convergence of the M\"obius-invariant Willmore flow in the 3-sphere, Part I

- Mathematics
- 2020

In this article the author continues his investigation of the M\"obius-invariant Willmore flow, for which the author has already proved existence and uniqueness of smooth short-time solutions,…

Total squared mean curvature of immersed submanifolds in a negatively curved space

- Mathematics
- 2021

Problems on the Willmore energy, i.e. the integral of the square of the mean curvature of submanifolds, in the Euclidean space and other space forms have a long history, around which many important…

The Willmore flow of Hopf-tori in the $3$-sphere

- Mathematics
- 2020

In this article the author investigates flow lines of the classical Willmore flow evolution equation (1) which start moving in a parametrization of a Hopf-torus in S. We prove that any such flow line…

Explicit formulas and symmetry breaking for Willmore surfaces of revolution

- Mathematics
- 2017

In this paper we prove explicit formulas for all Willmore surfaces of revolution and demonstrate their use in the discussion of the associated Dirichlet boundary value problems. It is shown by an…

Explicit formulas, symmetry and symmetry breaking for Willmore surfaces of revolution

- Mathematics
- 2017

In this paper, we prove explicit formulas for all Willmore surfaces of revolution and demonstrate their use in the discussion of the associated Dirichlet boundary value problems. It is shown by an…

Closed-forms of planar Kirchhoff elastic rods: application to inverse geometry

- Mathematics
- 2015

In this paper, we address the problem of inverse geometry for Kirchhoff elastic rods. Based on the explicit formulation of extremal curves in terms of elliptic functions, we derive closed forms for…

Numerical approximation of gradient flows for closed curves in Rd

- Mathematics
- 2010

We present parametric finite element approximations of curvature flows for
curves in Rd, d ≥ 2, as well as for curves on two-dimensional manifolds in R3.
Here we consider the curve shortening flow,…

The Constrained Blaschke Functional for Spherical Curves

- Mathematics
- 2022

We study critical trajectories in the sphere for the Blaschke variational problem with length constraint. For every Lagrange multiplier encoding the conservation of the length during the varia-tion,…

Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds

- MathematicsNumerische Mathematik
- 2021

Variational approximations of boundary value problems for curvature flow and elastic flow in two-dimensional Riemannian manifolds that are conformally flat are presented and natural boundary conditions that respect the appropriate gradient flow structure are proposed.