49 citations · 92 across the 19 of their papers we have counts for
22 papers
Existence of optimal flat ribbons
Simon Blatt, Matteo Raffaelli
We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in can be extended to an infinitely narrow flat ribbon having mini…
A fractional Willmore-type energy functional -- subcritical observations
Simon Blatt, Giovanni Giacomin, Julian Scheuer +1
We investigate surfaces with bounded L^p-norm of the fractional mean curvature, a quantity we shall refer to as fractional Willmore-type functional. In the subcritical case and und…
A regularized gradient flow for the -elastic energy
Simon Blatt, Christopher Hopper, Nicole Vorderobermeier
We prove long-time existence for the negative -gradient flow of the -elastic energy, , with an additive positive multiple of the length of the curve. To achieve th…
Scale-invariant tangent-point energies for knots
Simon Blatt, Philipp Reiter, Armin Schikorra +1
We investigate minimizers and critical points for scale-invariant tangent-point energies of closed curves. We show that a) minimizing sequences in ambient isotopy…
A minimising movement scheme for the -elastic energy of curves
Simon Blatt, Nicole Vorderobermeier, Christopher Hopper
We prove short-time existence for the negative -gradient flow of the -elastic energy of curves via a minimising movement scheme. In order to account for the degeneracy caus…
A Reverse Isoperimetric Inequality and its Application to the Gradient Flow of the Helfrich Functional
Simon Blatt
We prove a quantitative reverse isoperimetric inequality for embedded surfaces with Willmore energy bounded away from . We use this result to analyze the negative gradien…