4 papers
Calibration energy and mean curvature flow
Tatsuya Miura, Fabian Rupp
We introduce the calibration energy for oriented immersions into Euclidean space, quantifying the deviation from calibrated geometry. A key property is that this energy may remain…
A new energy method for shortening and straightening complete curves
Tatsuya Miura, Fabian Rupp
We introduce a novel energy method that reinterprets ``curve shortening'' as ``tangent aligning''. This conceptual shift enables the variational study of infinite-length curves evo…
Embeddedness and graphicality of the elastic flow for complete curves
Tatsuya Miura, Fabian Rupp
We study positivity-preserving properties for the elastic flow of non-compact, complete curves in Euclidean space. Despite the fact that the canonical elastic energy is infinite in…
Elastic bilayer membranes under confinement -- Existence, regularity, and rigidity
Matthias Röger, Fabian Rupp
Motivated by applications to cell biology, we study the constrained minimization of the Helfrich energy among closed surfaces confined to a container. We show existence of minimize…