Page 1 Lecture Notes in Mathematics Filippo Gazzola Hans-Christoph Grunau Guido Sweers
Polyharmonic Boundary Value Problems 1991 Positivity Preserving and Nonlinear Higher …

This review concerns the computation of curvature-dependent interface motion governed by
geometric partial differential equations. The canonical problem of mean curvature flow is that …

The Willmore conjecture, proposed in 1965, concerns the quest to find the best torus of all.
This problem has inspired a lot of mathematics over the years, helping bringing together …

We investigate point singularities of Willmore surfaces, which for example appear as
blowups of the Willmore flow near singularities, and prove that closed Willmore surfaces with …

Parametric finite elements lead to very efficient numerical methods for surface evolution
equations. We introduce several computational techniques for curvature driven evolution …

We show the existence of a global unique and analytic solution for the mean curvature flow,
the surface diffusion flow and the Willmore flow of entire graphs for Lipschitz initial data with …

We propose a new algorithm for the computation of Willmore flow. This is the L 2-gradient
flow for the Willmore functional, which is the classical bending energy of a surface. Willmore …

We present various variational approximations of Willmore flow in R^d, d=2,3. As well as the
classic Willmore flow, we also consider variants that are (a) volume preserving and (b) …

The equivalence of two approaches to the variational theory of cell-membrane equilibria
which have been proposed in the literature is demonstrated. Both assume a constraint on …

We consider the numerical solution of second order Partial Differential Equations (PDEs) on
lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the …