Yoshihito Kohsaka

Linearized Stability Analysis of Stationary Solutions for Surface Diffusion with Boundary Conditions

The linearizedstability of stationary solutions to the surface diffusion flow with angle conditions and no-flux conditions as boundary conditions is studied. We perform a linearized stability analysis in which the H-1 -gradient flow structure plays a key role. As a byproduct our analysis also gives a criterion for the stability of critical points of the length functional of curves which come into contact with the outer boundary. Finally, we study the linearized stability of several examples.

Nonlinear Stability of Stationary Solutions for Surface Diffusion with Boundary Conditions

The volume preserving fourth order surface diffusion flow has constant mean curvature hypersurfaces as stationary solutions. We show nonlinear stability of certain stationary curves in the plane which meet an exterior boundary with a prescribed contact angle. Methods include semigroup theory, energy arguments, geometric analysis and variational calculus.

Mean curvature flow with triple junctions in higher space dimensions

We consider mean curvature flow of n-dimensional surface clusters. At (n−1)-dimensional triple junctions an angle condition is required which in the symmetric case reduces to the well-known 120° angle condition. Using a novel parametrization of evolving surface clusters and a new existence and regularity approach for parabolic equations on surface clusters we show local well-posedness by a contraction argument in parabolic Hölder spaces.

Stability Analysis of Delaunay Surfaces as Steady States for the Surface Diffusion Equation

The stability of steady states for the surface diffusion equation will be studied. In the axisymmetric setting, steady states are the Delaunay surfaces, which are the axisymmetric constant mean curvature surfaces. We consider a linearized stability of these surfaces and derive criteria of the stability by investigating the sign of eigenvalues corresponding to the linearized problem.