Mean curvature flow with triple junctions in higher space dimensions

Abstract

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 degree 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 Hoelder spaces.

31 pages, 2 figures

References in corpus (1)

• Motion by Curvature of Planar Networks

Cited by in corpus (3)

• The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions
• On the existence of canonical multi-phase Brakke flows
• Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities