| Abstract: |
| In 1983, Kr\`{a}l proved the following theorem; \textit{Let $\Omega$ be a domain in $\mathbb{R}^n$. If $u \in C^1(\Omega)$ is harmonic in $\Omega \setminus u^{-1}(0) = \{ x \in \Omega \mid u(x) \ne 0 \}$, then $u$ is harmonic in the whole domain $\Omega$}. This type of removability results has been extensively studied in the literature. Among other things, we have studied the Kr\`{a}l type removability result for fully nonlinear equations. Our result in this talk is an extension of the previous one for the so-called $k$-Hessian equation and $k$-curvature equation. |
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