ANalysis and GEometry im Ländle -- Workshop am Fachbereich
Mathematik und Statistik der Universität Konstanz am Freitag,
18.07.2025
Freitag, 18.07.2025, ab 12:00 Uhr, Vorträge in Raum G 300
Programm
12:00: Treffen im Innenhof zwischen den Gebäuden A, B und
K,
Essen in der Mensa, nur Kartenzahlung
13:15-14:15: Manuel Schlierf, Ulm:Gradient flow dynamics for
cell membranes in the Canham-Helfrich model
The Canham-Helfrich model for the shape of lipid bilayers (such as
red blood cells) is one of the most prominent applications of the
variational study of Willmore-type bending energies. We study the
energetically most efficient way how a deformed red blood cell
regains equilibrium. This is mathematically described by the
gradient flow of the Canham-Helfrich functional, including a
spontaneous curvature and the conservation of surface area and
enclosed volume along the evolution. For the resulting non-local
geometric flow, in this talk I'll outline the main steps in the
proof of global existence and convergence of smooth solutions,
provided the initial energy lies below explicit thresholds.
14:15-15:00: Pause
15:00-16:00: Tim Laux, Heidelberg:
Generic level sets in mean curvature flow with and without
obstacles
Mean curvature flow has been a central object in geometric
analysis. Weak solutions describe the evolution past singularities,
but different solution concepts might lead to different behavior. In
this talk, I'll present recent results on the relation between the
viscosity solution and distributional solutions. I will also discuss
the associated obstacle problem, introduce solution concepts and
show their relation.
Based on joint work with Anton Ullrich (MPI MiS Leipzig), and with
Keisuke Takasao (University of Kyoto).
16:15-17:15: Lisa Beck, Augsburg:
Gradient integrability for bounded BD-minimizers
We consider functionals of the form
u ↦ ∫Ω f(ε(u)) dx
with a convex integrand f of linear growth, which
depends only on the symmetric part ε(u) of the
gradient, and
we study their minimization among all functions with prescribed
boundary values. Minimizing sequences are bounded in the space LD,
but they are not necessarily weakly relatively compact, due to
insufficient compactness properties of this space. Therefore, the
functional is extended suitably to the space BD of functions of
bounded deformation, where the existence of (BD-)minimizers can in
turn be guaranteed. Though the space BD is, by Ornstein’s
non-inequality, strictly larger than the space BV of functions of
bounded variation, Sobolev regularity of (BD-)minimizers can be
shown to hold for the same threshold on the lack of ellipticity as
in the full gradient case (which is relaxed to the space BV).
This talk is based on a joint project with Ferdinand Eitler
(Augsburg) and Franz Gmeineder (Konstanz).
17:30 oder 17:40: Bus von Konstanz Universität ↘
Konstanz Hauptbahnhof, 20 Minuten Fahrzeit
18:00: Abendessen in La Piazza, siehe
Stadtplan, direkt gegenüber des Hauptbahnhofs
Anmeldung für das Abendessen möglichst bis eine Woche vor
dem Meeting bei Elisabeth Greiler oder Oliver Schnürer (ü
→ ue):
Vorname.Nachname@uni-konstanz.de
