A nonexistence result on harmonic diffeomorphisms between punctured spaces

Abstract

In this paper, we will prove a result of nonexistence on harmonic diffeomorphisms between punctured spaces. In particular, we will given an elementary proof to the nonexistence of rotationally symmetric harmonic diffeomorphisms from the punctured Euclidean space onto the punctured hyperbolic space.

9 pages

References in corpus (2)

• Bi-Harmonic mappings and J. C. C. Nitsche type conjecture
• On J. C. C. Nitsche's type inequality for hyperbolic space ${\mathbf{H}}^3$

Cited by in corpus (1)

• An existence and uniqueness result for orientation-reversing harmonic diffeomorphism from ${\mathbb{H}}_{\ast }^n$ to ${\mathbb{R}}_{\ast }^n$