Xueshan Fu
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Xueshan Fu has a total of 9 co-authors. Here are the top co-authors by number of shared publications:
- Jinhua Qian
Northeastern University
12 shared publications - Seoung Dal Jung
Department of Mathematics, Jeju National University, Jeju, Republic of Korea
11 shared publications - Xueqian Tian
Department of Mathematics, Northeastern University, Shenyang 110004, China
2 shared publications - Young Ho Kim
Kyungpook National University
2 shared publications - Hongzeng Wang
Northeastern Univ, Dept Math, Shenyang, Peoples R China
1 shared publication - Huili Liu
Department of Mathematics, Northeastern University, Shenyang, People’s Republic of China
1 shared publication
Latest Publications
- 6 June 2024
- Published by Elsevier in Journal of Geometry and Physics
- Vol. 203
Weighted p-basic harmonic forms and its applications
- 6 June 2024
- Published by Elsevier in Journal of Geometry and Physics
- Vol. 203
Weighted p-basic harmonic forms and its applications
- Open Access
Generalized Chen's conjecture for biharmonic maps on foliations
In this paper, we prove the generalized Chen's conjecture for (F,F')-biharmonic map, which is a critical point of the transversal bienergy functional
Open AccessGeneralized Chen's conjecture for biharmonic maps on foliations
In this paper, we prove the generalized Chen's conjecture for (F,F')-biharmonic map, which is a critical point of the transversal bienergy functional
- Open Access
Harmonic maps on weighted Riemannian foliations
On foliations, there are two kinds of harmonic maps, that is, transversally harmonic map and $(F,F')$-harmonic map which are equivalent when the foliation is minimal. In this paper, we study transversally f-harmonic and $(F,F')_f$-harmonic maps on weighted foliations.
Open AccessHarmonic maps on weighted Riemannian foliations
On foliations, there are two kinds of harmonic maps, that is, transversally harmonic map and $(F,F')$-harmonic map which are equivalent when the foliation is minimal. In this paper, we study transversally f-harmonic and $(F,F')_f$-harmonic maps on weighted foliations.
- Open Access
- 1 June 2023
- Published by Springer Nature in Mathematische Annalen
- Vol. 389 (1) , 187-208
Generalized Hasimoto-type surfaces of null growth in Minkowski 3-space
In this article, the idea of the generalized Hasimoto-type surfaces are put forward based on the interaction between vortex filaments. Meanwhie, the surface of null growth is proposed by evolving a null curve as dictated direction and growth velocity in Minkowski 3-space. The conditions and geometric forms of the generalized Hasimoto-type surfaces of null growth are investigated. Last but not least, several typical examples are presented to characterize such surface growth and the corresponding perturbations explicitly.
- 1 June 2023
- Published by Springer Nature in Mathematische Annalen
- Vol. 389 (1) , 187-208
Open AccessGeneralized Hasimoto-type surfaces of null growth in Minkowski 3-space
In this article, the idea of the generalized Hasimoto-type surfaces are put forward based on the interaction between vortex filaments. Meanwhie, the surface of null growth is proposed by evolving a null curve as dictated direction and growth velocity in Minkowski 3-space. The conditions and geometric forms of the generalized Hasimoto-type surfaces of null growth are investigated. Last but not least, several typical examples are presented to characterize such surface growth and the corresponding perturbations explicitly.
- 20 April 2023
- Published by Springer Nature in Results in Mathematics
- Vol. 78 (4) , 1-21
Liouville Type Theorem for $({\mathcal {F}},{\mathcal {F}}')_{p}$-Harmonic Maps on Foliations- 20 April 2023
- Published by Springer Nature in Results in Mathematics
- Vol. 78 (4) , 1-21
Liouville Type Theorem for $({\mathcal {F}},{\mathcal {F}}')_{p}$-Harmonic Maps on Foliations- Open Access
- 6 February 2023
- Published by Springer Nature in Research Square
Harmonic maps on weighted foliations
On foliations, there are two kinds of harmonic maps, that is, transversallyharmonic map and (F,F')-harmonic map which are equivalent when the foliation is minimal. In this paper, we study transversally ƒ-harmonic and (F,F')ƒ-harmonic maps on weightedfoliations. Moreover, we investigate the relations between transversal stress energy tensorsand tranversally ƒ-harmonic maps.
- 6 February 2023
- Published by Springer Nature in Research Square
Open AccessHarmonic maps on weighted foliations
On foliations, there are two kinds of harmonic maps, that is, transversallyharmonic map and (F,F')-harmonic map which are equivalent when the foliation is minimal. In this paper, we study transversally ƒ-harmonic and (F,F')ƒ-harmonic maps on weightedfoliations. Moreover, we investigate the relations between transversal stress energy tensorsand tranversally ƒ-harmonic maps.
- Open Access
Liouville type theorem for (F;F')p-harmonic maps on foliations
In this paper, we study $(\mathcal F,\mathcal F')_{p}$-harmonic maps between foliated Riemannian manifolds $(M,g,\mathcal F)$ and $(M',g',\mathcal F')$. A $(\mathcal F,\mathcal F')_{p}$-harmonic map $\phi:(M,g,\mathcal F)\to (M', g',\mathcal F')$ is a critical point of the transversal $p$-energy functional $E_{B,p}$. Trivially, $(\mathcal F,\mathcal F')_2$-harmonic map is $(\mathcal F,\mathcal F')$-harmonic map, which is a critical point of $E_B$. There is another definition of a harmonic map on foliated Riemannian manifolds, called transversally harmonic map, which is a solution of the Euler-Largrange equation $\tau_b(\phi)=0$. Two definitions are not equivalent, but if $\mathcal F$ is minimal, then two definitons are equivalent. Firstly, we give the first and second variational formulas for $(\mathcal F,\mathcal F')_{p}$-harmonic maps. Next, we investigate the generalized Weitzenb\"ock type formula and the Liouville type theorem for $(\mathcal F,\mathcal F')_{p}$-harmonic map.Open AccessLiouville type theorem for (F;F')p-harmonic maps on foliations
In this paper, we study $(\mathcal F,\mathcal F')_{p}$-harmonic maps between foliated Riemannian manifolds $(M,g,\mathcal F)$ and $(M',g',\mathcal F')$. A $(\mathcal F,\mathcal F')_{p}$-harmonic map $\phi:(M,g,\mathcal F)\to (M', g',\mathcal F')$ is a critical point of the transversal $p$-energy functional $E_{B,p}$. Trivially, $(\mathcal F,\mathcal F')_2$-harmonic map is $(\mathcal F,\mathcal F')$-harmonic map, which is a critical point of $E_B$. There is another definition of a harmonic map on foliated Riemannian manifolds, called transversally harmonic map, which is a solution of the Euler-Largrange equation $\tau_b(\phi)=0$. Two definitions are not equivalent, but if $\mathcal F$ is minimal, then two definitons are equivalent. Firstly, we give the first and second variational formulas for $(\mathcal F,\mathcal F')_{p}$-harmonic maps. Next, we investigate the generalized Weitzenb\"ock type formula and the Liouville type theorem for $(\mathcal F,\mathcal F')_{p}$-harmonic map. - 24 November 2021
- Published by Springer Nature in Journal of Geometry
- Vol. 113 (1) , 1-9
Liouville type theorem for transversally harmonic maps
- 24 November 2021
- Published by Springer Nature in Journal of Geometry
- Vol. 113 (1) , 1-9
Liouville type theorem for transversally harmonic maps
- Open Access
- 21 June 2021
- Published by MDPI AG in Mathematics
- Vol. 9 (12) , 1451
Representations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space
In this work, the rectifying isotropic curves are investigated in three-dimensional complex space . The conclusion that an isotropic curve is a rectifying curve if and only if its pseudo curvature is a linear function of its pseudo arc-length is achieved. Meanwhile, the rectifying isotropic curves are expressed by the Bessel functions explicitly. Last but not least, the centrodes of rectifying isotropic curves are explored in detail.- 21 June 2021
- Published by MDPI AG in Mathematics
- Vol. 9 (12) , 1451
Open AccessRepresentations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space
In this work, the rectifying isotropic curves are investigated in three-dimensional complex space . The conclusion that an isotropic curve is a rectifying curve if and only if its pseudo curvature is a linear function of its pseudo arc-length is achieved. Meanwhile, the rectifying isotropic curves are expressed by the Bessel functions explicitly. Last but not least, the centrodes of rectifying isotropic curves are explored in detail. - Open Access
- 2 November 2020
- Published by MDPI AG in Mathematics
- Vol. 8 (11) , 1921
Representation of Maximal Surfaces in a 3-Dimensional Lightlike Cone
In this paper, the representation formula of maximal surfaces in a 3-dimensional lightlike cone is obtained by making use of the differential equation theory and complex function theory. Some particular maximal surfaces under a special induced metric are presented explicitly via the representation formula.- 2 November 2020
- Published by MDPI AG in Mathematics
- Vol. 8 (11) , 1921
Open AccessRepresentation of Maximal Surfaces in a 3-Dimensional Lightlike Cone
In this paper, the representation formula of maximal surfaces in a 3-dimensional lightlike cone is obtained by making use of the differential equation theory and complex function theory. Some particular maximal surfaces under a special induced metric are presented explicitly via the representation formula.