29 citations · 78 across the 22 of their papers we have counts for
8 papers · 1 filter
Generalized Ricci flow I: Local existence and uniqueness
Chun-lei He, Sen Hu, De-Xing Kong +1
In this paper we investigate a kind of generalized Ricci flow which possesses a gradient form. We study the monotonicity of the given function under the generalized Ricci flow and…
Hyperbolic Gradient Flow: Evolution of Graphs in R^{n+1}
De-Xing Kong, Kefeng Liu
In this paper we introduce a new geometric flow --- the hyperbolic gradient flow for graphs in the -dimensional Euclidean space . This kind of flow is new…
Life-span of classical solutions to hyperbolic geometric flow in two space variables with slow decay initial data
De-Xing Kong, Kefeng Liu, Yu-Zhu Wang
In this paper we investigate the life-span of classical solutions to the hyperbolic geometric flow in two space variables with slow decay initial data. By establishing some new est…
Hyperbolic Mean Curvature Flow
Chun-Lei He, De-Xing Kong, Kefeng Liu
In this paper we introduce the hyperbolic mean curvature flow and prove that the corresponding system of partial differential equations are strictly hyperbolic, and based on this,…
Hyperbolic mean curvature flow: Evolution of plane curves
De-Xing Kong, Kefeng Liu, Zeng-Gui Wang
In this paper we investigate the one-dimensional hyperbolic mean curvature flow for closed plane curves. We show that there exists a class of initial velocities such that the solut…
Dissipative Hyperbolic Geometric Flow
Wen-Rong Dai, De-Xing Kong, Kefeng Liu
In this paper we introduce and study a new kind of hyperbolic geometric flows --dissipative hyperbolic geometric flow. This kind of flow is defined by a system of quasilinear wave…
The hyperbolic geometric flow on Riemann surfaces
De-Xing Kong, Kefeng Liu, De-Liang Xu
In this paper the authors study the hyperbolic geometric flow on Riemann surfaces. This new nonlinear geometric evolution equation was recently introduced by the first two authors…
Hyperbolic geometric flow (I): short-time existence and nonlinear stability
Wen-Rong Dai, De-Xing Kong, Kefeng Liu
In this paper we establish the short-time existence and uniqueness theorem for hyperbolic geometric flow, and prove the nonlinear stability of hyperbolic geometric flow defined on…