16 citations · 33 across the 13 of their papers we have counts for
13 papers
Domain decomposition methods with Physics-informed neural networks for elliptic equations on manifolds
Yufang Jiang, Lizhen Qin, Feng Wang
We propose two numerical domain decomposition methods (DDMs) for elliptic equations on compact Riemannian manifolds, based on physics-informed neural networks (PINNs). Our approach…
Self-covering, finiteness, commutativity, and fibering over tori
Lizhen Qin, Yang Su
A topological space is called self-covering if it is a nontrivial cover of itself. We prove that, under mild assumptions, a closed self-covering manifold with an abelian fundamenta…
A parallel domain decomposition method for solving elliptic equations on manifolds
Lizhen Qin, Feng Wang, Yun Wang
We propose a new numerical domain decomposition method for solving elliptic equations on compact Riemannian manifolds. One advantage of this method is its ability to bypass the nee…
-Biharmonic submanifolds in space forms and -biharmonic Riemannian submersions from 3-manifolds
Ze-Ping Wang, Li-Hua Qin
-Biharmonic maps are generalizations of harmonic maps and biharmonic maps. In this paper, we obtain some descriptions of -biharmonic curves in a space form. We also obtain a…
A numerical domain decomposition method for solving elliptic equations on manifolds
Shuhao Cao, Lizhen Qin
A new numerical domain decomposition method is proposed for solving elliptic equations on compact Riemannian manifolds. The advantage of this method is to avoid global triangulatio…
Self-Covering, finiteness, and fibering over a circle
Lizhen Qin, Yang Su, Botong Wang
A topological space is called self-covering if it is a nontrivial cover of itself. We prove that a closed self-covering manifold with free abelian fundamental group fibers over…
On the various notions of Poincaré duality pair
John R. Klein, Lizhen Qin, Yang Su
We establish a number of foundational results on Poincaré spaces which result in several applications. One application settles an old conjecture of C.T.C. Wall in the affirmative.…
A Family of Compact Complex-Symplectic Calabi-Yau Manifolds that are Nonkähler
Lizhen Qin, Botong Wang
We construct a family of -dimensional compact manifolds , which are simultaneously diffeomorphic to complex Calabi-Yau manifolds and symplectic Calabi-Yau manifolds. They…
On some 1/4 BPS Wilson-'t Hooft loops
Chang-Yong Liu, Li Qin
In this paper, we investigate the 1/4 BPS Wilson-'t Hooft loops in =4 supersymmetric Yang-Mills theory. We use the bulk D3-brane solutions with both electric and magne…
A Geometric Proof of Removal of Boundary Singularities of Pseudo-Holomorphic Curves
Urs Fuchs, Lizhen Qin
We prove two theorems on the removal of singularities on the boundary of a pseudo-holomorphic curve. In one theorem, we need no apriori assumption on the area of the curve. The pro…
On the Associativity of Gluing
Lizhen Qin
This paper studies the associativity of gluing of trajectories in Morse theory. We show that the associativity of gluing follows from of the existence of compatible manifold with f…
An application of topological equivalence to Morse theory
Lizhen Qin
In a previous paper, under the assumption that the Riemannian metric is special, the author proved some results about the moduli spaces and CW structures arising from Morse theory.…
On Moduli Spaces and CW Structures Arising from Morse Theory On Hilbert Manifolds
Lizhen Qin
This paper proves some results on negative gradient dynamics of Morse functions on Hilbert manifolds. It contains the compactness of flow lines, manifold structures of certain comp…