3 papers
math.AP2020
Lower regularity assumption for an Euler-Lagrange equation on the contact line of the phase dependent Helfrich energy
Sascha Eichmann
We examine the phase dependent Helfrich energy and show an Euler-Lagrange equation on the phase seperation line. This result has already been observed by e.g. Jülicher-Lipowski and…
math.AP2019
Lower-semicontinuity for the Helfrich problem
Sascha Eichmann
We minimise the Canham-Helfrich energy in the class of closed immersions with prescribed genus, surface area and enclosed volume. Compactness is achieved in the class of oriented v…
math.AP2018
The Helfrich Boundary Value Problem
Sascha Eichmann
We construct a branched Helfrich immersion satisfying Dirichlet boundary conditions. The number of branch points is finite. We proceed by a variational argument and hence examine t…