Free Boundary Problems 2026

Session

Geometric Flows and Evolving Free Boundaries

MS-2

7 Sept 2026, 14:00

Humboldt Universität zu Berlin

Conveners

Geometric Flows and Evolving Free Boundaries: MS-2-1

• Sebastian Hensel

Description

Organisers: Sebastian Hensel

82. The area preserving curve shortening flow with Neumann free boundary conditions

Elena Mäder-Baumdicker (Freie Universität Berlin)

07/09/2026, 14:00

Geometric Flows and Evolving Free Boundaries

The area preserving curve shortening flow with Neumann free boundary conditions shortens a curve that is attached perpendicularly to a bounded domain $\Omega$ in the plane but keeps the enclosed area fixed. The end points of that curve move in the boundary curve of $\Omega$. Its limits are candidates for minimizers for the relative isoperimetric problem in the plane (thus, they are circular...

100. On the two-phase Mullins--Sekerka flow: Convergence and Existence

Saša Lukić (RWTH Aachen University)

07/09/2026, 14:30

Geometric Flows and Evolving Free Boundaries

In this talk, we discuss up to two different aspects of the two-phase Mullins--Sekerka evolution.

In the first part, we investigate the convergence to equilibrium configurations: It is well-known that nearly spherical interfaces given as nearly radial graphs over spheres converge to an equilibrium configuration exponentially fast with a rate $\sim 1/R^3$, where $R$ is the radius of the...

13. De Giorgi varifold solutions to Volume Preserving Mean Curvature Flow

Andrea Poiatti (University of Parma)

07/09/2026, 15:00

Geometric Flows and Evolving Free Boundaries

In this talk, I would like to introduce a novel weak solution concept for two-phase Volume Preserving Mean Curvature Flow, having both properties of unconditional global-in-time existence and weak-strong uniqueness. These solutions consist in evolving varifolds coupled with the phase volumes by a transport equation. We preliminarily concentrate on the existence, showing first that any sharp...

43. Quantitative homogenization of forced geometric motions through random fields of obstacles

Jonas Ingmanns (Institute of Science and Technology Austria)

07/09/2026, 15:30

Geometric Flows and Evolving Free Boundaries

Consider the evolution of sets by forced mean curvature flow through a field of random obstacles. The effective large scale behaviour is expected to be a first order motion. However, previous results heavily relied on the assumption that there is a global minimum speed of expansion and hence on the absence of any actual obstacles.

We obtain a quantitative homogenization result even with...