Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 85, pp. 1-5.

Title: Remark on isolated removable singularities of harmonic maps in two dimensions

Author: Changyou Wang (Purdue Univ., West Lafayette, IN, USA)

Abstract:
For a ball $B_R(0)\subset\mathbb{R}^2$, we provide sufficient conditions such that
a harmonic map $u\in C^\infty(B_R(0)\setminus\{0\}, N)$, with a self-similar bound
on its gradient,  belong to $C^\infty(B_R(0))$.
These conditions also guarantee the triviality of such harmonic maps when $R=\infty$.

Submitted April 18, 2025. Published August 11, 2025.
Math Subject Classifications: 35J50, 58E20.
Key Words: Harmonic maps; removable isolated singularity.