Sze-Man Ngai

activity

20242026

collaborators

6 papers

math.FA2026

Krein-Feller operators on Riemannian manifolds: compactness of embedding and Hodge's theorem

Sze-Man Ngai, Lei Ouyang

For a bounded open set Omega in a complete oriented Riemannian n-manifold and a positive finite Borel measure mu with support contained in Omega, we define an associated Krein-Fell…

math.DG2025

Hodge-de Rham Theory on Higher-Dimensional Level-L Sierpinski Gaskets

Sze-Man Ngai, Shui-Hong Zhou

This paper extends the Hodge-de Rham theory of Aaron \textit{et al.} [Commun. Pure Appl. Anal. {\bf 13} (2014)] to higher-dimensional level- $l$ Sierpinski gaskets $S G_{ℓ}^{n},$ …

math.DS2024

Iterated relation systems on Riemannian manifolds

Jie Liu, Sze-Man Ngai, Lei Ouyang

For fractals on Riemannian manifolds, the theory of iterated function systems often does not apply well directly, as fractal sets are often defined by relations that are multivalue…

math.FA2024

Nodal sets and continuity of eigenfunctions of Krein-Feller operators on Riemannian manifolds

Sze-Man Ngai, Wen-Quan Zhao

Let $d \geq 1$ , $I^c ◯$ be a bounded domain of a smooth complete Riemannian d-manifold M, and $I^¼$ be a positive finite Borel measure with compact support in $I^c ◯$ . We prove the…

math.AP2024

Nodal sets and continuity of eigenfunctions of Kre\uÄ±-Feller operators

Sze-Man Ngai, Meng-Ke Zhang, Wen-Quan Zhao

Let $I^¼$ be a compactly supported positive finite Borel measure on $R^{d}$ . Let $0 < I^»_{1} \leq I^»_{2} \leq \dots$ be eigenvalues of the Kre $A ¨ \pm ˘$ n-Feller operator $I^_{I^} ¼$ . We p…

math.FA2024

Differential equations defined by Kre\uÄ±n-Feller operators on Riemannian manifolds

Sze-Man Ngai, Lei Ouyang

We study linear and semi-linear wave, heat, and SchrÃ¶dinger equations defined by Kre\uÄ±n-Feller operator $- I^_{I^} ¼$ on a complete Riemannian $n$ -manifolds $M$ , where $I^¼$ is a fini…