Dirichlet problem for harmonic maps from strongly rectifiable spaces into regular balls in \CAT(1) spaces

2022/08/15 by Yohei Sakurai, Sakurai, Yohei
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2208.07150

Abstract

In this note, we study the Dirichlet problem for harmonic maps from strongly rectifiable spaces into regular balls in \CAT(1) space. Under the setting, we prove that the Korevaar-Schoen energy admits a unique minimizer.

Related

• Korevaar-Schoen's energy on strongly rectifiable spaces
• Existence of harmonic maps into CAT(1) spaces
• Generic non-uniqueness of minimizing harmonic maps from a ball to a sphere
• Existence of p harmonic multiple valued maps into a separable Hilbert\n space
• Regularity of Harmonic Maps from Polyhedra to CAT(1) Spaces