7 citations · 18 across the 15 of their papers we have counts for
17 papers
Yang-Mills-Higgs-Schrödinger flow
Bo Chen, Chong Song
In this paper, we initiate the study of the Yang-Mills-Higgs-Schrödinger(YMHS) flow, i.e. the Hamiltonian flow of the Yang-Mills-Higgs functional defined on a symplectic fiber bund…
Correspondence between Mean Curvature Flow and Harmonic-Ricci Flow
Tianyin Ren, Chong Song
In this paper, we observe that the (spacelike) mean curvature flow of a submanifold in a (pseudo-)Euclidean space is equivalent to a harmonic-Ricci flow with coupling constant $α=-…
Isolated singularities of 3-dimensional Yang-Mills-Higgs fields
Bo Chen, Chong Song
In this paper, we derive decay estimates near isolated singularities of 3-dimensional (3d) Yang-Mills-Higgs fields defined on a fiber bundle, where the fiber space is a compact Rie…
Harmonic map flow for almost-holomorphic maps
Chong Song, Alex Waldron
Let be a compact oriented surface and a compact Kähler manifold with nonnegative holomorphic bisectional curvature. For a solution of harmonic map flow starting from an alm…
Isolated Singularities of Yang-Mills-Higgs fields on surfaces
Bo Chen, Chong Song
We study isolated singularities of two dimensional Yang-Mills-Higgs fields defined on a fiber bundle, where the fiber space is a compact Riemannian manifold and the structure group…
Local existence and uniqueness of Skew Mean Curvature Flow
Chong Song
The Skew Mean Curvature Flow(SMCF) is a Schrödinger-type geometric flow canonically defined on a co-dimension two submanifold, which generalizes the famous vortex filament equation…
Harmonic maps with free boundary from degenerating bordered Riemann surfaces
Lei Liu, Chong Song, Miaomiao Zhu
We study the blow-up analysis and qualitative behavior for a sequence of harmonic maps with free boundary from degenerating bordered Riemann surfaces with uniformly bounded energy.…
Gauss map of the skew mean curvature flow
Chong Song
The skew mean curvature flow (SMCF) is a natural generalization of the famous vortex filament equation. In this note, we show that the Gauss map of the SMCF satisfies a Schrödinger…
Uniqueness of Schrödinger flow on manifolds
Chong Song, Youde Wang
In this paper, we show the uniqueness of Schrödinger flow from a general complete Riemannian manifold to a complete Kähler manifold with bounded geometry. While following the ideas…
The boundary value problem for Yang--Mills--Higgs fields
Wanjun Ai, Chong Song, Miaomiao Zhu
We show the existence of Yang--Mills--Higgs (YMH) fields over a Riemann surface with boundary where a free boundary condition is imposed on the section and a Neumann boundary condi…
Hessian estimates for convex solutions to quadratic Hessian equation
Matt McGonagle, Chong Song, Yu Yuan
We derive Hessian estimates for convex solutions to quadratic Hessian equation by a compactness argument.
Heat flow of Yang-Mills-Higgs functionals in dimension two
Chong Song, Changyou Wang
We consider the heat flow of Yang-Mills-Higgs functional where the base manifold is a Riemannian surface and the fiber is a compact symplectic manifold. We show that the correspond…
Skew Mean Curvature Flow
Chong Song, Jun Sun
The skew mean curvature flow(SMCF), which origins from the study of fluid dynamics, describes the evolution of a codimension two submanifold along its binormal direction. We study…
Convergence of Yang-Mills-Higgs fields
Chong Song
In this paper, we study the convergence of Yang-Mills-Higgs fields defined on fiber bundles over Riemann surfaces where the fiber is a compact symplectic manifold and the conformal…
Geometric solitons of Hamiltonian flows on manifolds
Chong Song, Xiaowei Sun, Youde Wang
It is well-known that the LIE(Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By…
Generalized Landau-Lifshitz Equation into
Chong Song, Jie Yu
In this paper, a type of integrable evolution equation--the generalized Landau-Lifshitz equation into is considered. We deal with this equation from a geometric point of view…
Schrödinger Soliton from Lorentzian Manifolds
Chong Song, Youde Wang
In this paper, we introduce a new notion named as Schrödinger soliton. So-called Schrödinger solitons are defined as a class of special solutions to the Schrödinger flow equation f…