2 citations · 10 across the 8 of their papers we have counts for
9 papers · 1 filter
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…
Analyticity for Solution of Integro-Differential Operators
Simon Blatt
We prove that for a certain class of kernels that viscosity solutions of the integro-differential equation $$ \int_{\mathbb R^n} (u(x+y) - 2 u(x) + u(x-y)) K(y) dy = f(x,u(x…
On O'hara knot energies I: Regularity for critical knots
Simon Blatt, Philipp Reiter, Armin Schikorra
We develop a regularity theory for extremal knots of scale invariant knot energies defined by J. O'hara in 1991. This class contains as a special case the Möbius energy. For the Mö…