4 papers
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…
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…