arXiv subjects

Hyunsoo Ahn

Publications and source records attributed to Hyunsoo Ahn.

3 recordsLinked to original sources

arXiv2026

Characterization of continuity of Siciak-Zaharjuta extremal functions on compact Hermitian manifolds

For a compact subset in a compact Hermitian manifold, we prove that the continuity of the extremal function at a given point in the set is a local property and that the continuity of a weighted extremal function follows from the continuities of the extremal function and the weight function. These results are generalizations of the results of Nguyen \cite{Ng24} on compact K\"ahler manifolds. Moreover, for a compact subset in a compact Hermitian manifold, at the point level and accordingly at the global level, we characterize the continuity of the extremal function via the local $L$-regularity, which is equivalent to the weak local $L$-regularity. We also show that the $L$-regularity of a compact subset in $\mathbb{C}^n$ at a star center implies the local $L$-regularity. Consequently, a convex compact $L$-regular subset in $\mathbb{C}^n$ is locally $L$-regular.

math.CV↗

arXiv2026

H\"older regularity of Siciak-Zaharjuta extremal functions on compact Hermitian manifolds

For a compact subset in a compact Hermitian manifold, we prove that the H\"older continuity of the extremal function at a given point in the set is a local property and that the H\"older continuity of a weighted extremal function follows from the H\"older continuities of the extremal function and the weight function with a uniform density in capacity. The second result can be seen as a continuation of a result of Lu, Phung and T\^o \cite{LPT21}. Moreover, for a compact subset in a compact Hermitian manifold, we prove that, both at the point level and at the global level, the H\"older continuity of the extremal function with the uniform density in capacity is equivalent to the local H\"older continuity property, which is also equivalent to the weak local H\"older continuity property. These results are generalizations of the results of Nguyen \cite{Ng24} on compact K\"ahler manifolds. We also show that the $\mu$-H\"older continuity property of a convex compact subset in $\mathbb{C}^n$ and of a compact subset in $\mathbb{C}^n$ at a star center imply the local $\mu$-H\"older continuity property of order $\mu$ of the convex compact subset and of the compact subset at the point, respectively.

math.CV↗

arXiv2024

Convergence Speed for Fekete Points on Uniformly Polynomially Cuspidal Sets

We obtain the convergence speed for Fekete points on uniformly polynomially cuspidal compact sets introduced by Pawlucki and Ple\'sniak. This is done by showing that these sets are $(\mathscr{C}^{\alpha}, \mathscr{C}^{\alpha'})$-regular in the sense of Dinh, Ma and Nguyen.

math.CV↗