2008/12/08 by Alexandre Freire, Freire, Alexandre
Mathematics · #35K55 #53C44 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.AP #msc:35K55 #msc:53C44
paper · pdf · doi:10.48550/arxiv.0812.1573
Revised version of the preprint with similar title posted in May 2008
arxiv created 2008/12/08 · openalex publication_date 2008/12/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the motion by mean curvature of an n-dimensional graph over a time-dependent domain in ℝn, intersecting ℝn at a constant angle. In the general case, we prove local existence for the corresponding quasilinear parabolic equation with a free boundary, and derive a continuation criterion based on the second fundamental form. If the initial graph is concave, we show this is preserved, and that the solution exists only for finite time. This corresponds to a symmetric version of mean curvature motion of a network of hypersurfaces with triple junctions, with constant contact angle at the junctions.