3 papers
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- Sierpinski gaskets …
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
Hodge Theorem for Krein-Feller operators on compact Riemannian manifolds
Sze-Man Ngai, Lei Ouyang
For an open set in a compact smooth oriented Riemannian n-manifold and a positive finite Borel measure with support contained in the closure of the open set, we define an associate…