18 citations · 19 across the 10 of their papers we have counts for
11 papers
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 …
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…
Nodal sets and continuity of eigenfunctions of Krein-Feller operators on Riemannian manifolds
Sze-Man Ngai, Wen-Quan Zhao
Let , be a bounded domain of a smooth complete Riemannian d-manifold M, and be a positive finite Borel measure with compact support in . We prove the Co…
Nodal sets and continuity of eigenfunctions of Kre\uı-Feller operators
Sze-Man Ngai, Meng-Ke Zhang, Wen-Quan Zhao
Let be a compactly supported positive finite Borel measure on . Let be eigenvalues of the Kren-Feller operator . We prove t…
Differential equations defined by Kre\uın-Feller operators on Riemannian manifolds
Sze-Man Ngai, Lei Ouyang
We study linear and semi-linear wave, heat, and Schrödinger equations defined by Kre\uın-Feller operator on a complete Riemannian -manifolds , where is a finite po…
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…
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…
Separation conditions for iterated function systems with overlaps on Riemannian manifolds
Sze-Man Ngai, Yangyang Xu
We formulate the weak separation condition and the finite type condition for conformal iterated function systems on Riemannian manifolds with nonnegative Ricci curvature, and gener…
A class of self-affine tiles in that are -dimensional tame balls
Guotai Deng, Chuntai Liu, Sze-man Ngai
We study a family of self-affine tiles in () with noncollinear digit sets, which naturally generalizes a class studied originally by Deng and Lau in $\mathbb{…
Existence of -dimension and entropy dimension of self-conformal measures on Riemannian manifolds
Sze-Man Ngai, Yangyang Xu
Peres and Solomyak proved that on , the limits defining the -dimension for any , and the entropy dimension of a self-conformal measu…
One-dimensional wave equations defined by fractal Laplacians
John Fun-Choi Chan, Sze-Man Ngai, Alexander Teplyaev
We study one-dimensional wave equations defined by a class of fractal Laplacians. These Laplacians are defined by fractal measures generated by iterated function systems with overl…