A variational approach to the regularity of minimal surfaces of annulus type in Riemannian manifolds

2006/03/27 by Kim, Hwajeong
#49Q05 #58E05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0603610

Abstract

Given two Jordan curves in a Riemannian manifold, a minimal surface of annulus type bounded by these curves is described as the harmonic extension of a critical point of some functional (the Dirichlet integral) in a certain space of boundary parametrizations. The H^2,2-regularity of the minimal surface of annulus type will be proved by applying the critical points theory and Morrey's growth condition.

Related

• Unstable minimal surfaces of annulus type in manifolds
• Local uniformization and free boundary regularity of minimal singular surfaces
• Harmonic maps with prescribed degrees on the boundary of an annulus and\n bifurcation of catenoids
• A Note On Free Boundary Minimal Annulus
• Regularity of sets of least perimeter in Riemannian manifolds