An existence theorem for sliding minimal sets

2025/10/02 by Guy David, Camille Labourie, David, Guy +1
Computer Science · #49K99 #49Q20 #Artificial Intelligence in Games #Classical Analysis and ODEs (math.CA) #Computational Geometry and Mesh Generation #FOS: Mathematics #Robotic Path Planning Algorithms

paper · pdf · doi:10.48550/arxiv.2510.01905

openalex publication_date 2025/10/02 · openalex created_date 2025/10/04 · openalex updated_date 2026/07/28

Abstract

We prove an existence theorem for the sliding boundary variant of the Plateau problem for 2-dimensional sets in ℝⁿ. The simplest case of sufficient condition is when n=3 and the boundary Γ is a finite disjoint union of smooth closed curves contained in the boundary of a convex body, but the main point of our sufficient condition is to prevent the limits in measure of a minimizing sequence to have singularities of type \mathbbY along Γ.

Related

• Sliding almost minimal sets and the Plateau problem
• Existence and regularity results for minimal sets; Plateau problem
• Local C^1,β-regularity at the boundary of two dimensional sliding almost minimal sets in ℝ³
• Sliding minimal cones in the 3-dimensional half-space
• Hölder regularity at the boundary of two-dimensional sliding almost minimal sets