Let $u:\mathbb{S}^{n-1}\mapsto\mathbb{R}^n$ be an orientation preserving $(C^1)$ map. Is it true that it's harmonic extension $u_h:B_1\mapsto\mathbb{R}^n$, namely the map that is such that $\Delta u_h=0$ in $B_1$ and $u_h=u$ on $\mathbb{S}^{n-1}$, is orientation preserving as well?
Asked
Active
Viewed 31 times
